Tüm alıştırma soruları

Soru 421Soru →

A structural blueprint for a new commercial warehouse uses a scale of $\frac{1}{2}\text{ inch} = 15\text{ feet}$ . On the blueprint, the rectangular main storage floor measures $3\frac{1}{3}\text{ inches}$ in length and $2\frac{1}{5}\text{ inches}$ in width. What is the actual area of the main storage floor in square feet?

Cevabı ve açıklamayı göster

Cevap: 6600

Cevap

The actual area of the main storage floor is 6600 square feet.

To find the actual area, we first establish the true scale of the blueprint. Since

\frac{1}{2}\text{ inch}

represents

15\text{ feet}

,

1\text{ inch}

represents

30\text{ feet}

. The blueprint dimensions are given as mixed fractions:

3\frac{1}{3}\text{ inches}

and

2\frac{1}{5}\text{ inches}

. We convert these to the improper fractions

\frac{10}{3}

and

\frac{11}{5}

, and multiply each by the scale factor of

30

to find the actual dimensions. The actual length is

\frac{10}{3} \times 30 = 100\text{ feet}

, and the actual width is

\frac{11}{5} \times 30 = 66\text{ feet}

. Finally, the area of the rectangle is found by multiplying the actual length by the actual width, yielding

100 \times 66 = 6600\text{ square feet}

.

Adım Adım Çözüm

1

Determine the unit scale rate.

1\text{ inch} = 30\text{ feet}

The scale is given as

\frac{1}{2}\text{ inch} = 15\text{ feet}

. Multiplying both sides by

2

provides the actual distance per single inch on the drawing.

2

Calculate the actual length of the storage floor.

100\text{ feet}

Convert

3\frac{1}{3}

to the improper fraction

\frac{10}{3}

, then multiply by the scale factor of

30

:

\frac{10}{3} \times 30 = 100

.

3

Calculate the actual width of the storage floor.

66\text{ feet}

Convert

2\frac{1}{5}

to the improper fraction

\frac{11}{5}

, then multiply by the scale factor of

30

:

\frac{11}{5} \times 30 = 66

.

4

Calculate the actual area of the rectangular floor.

6600\text{ square feet}

Area is found by multiplying the actual length by the actual width:

100 \times 66 = 6600

.

Anahtar Kavram

Scale Drawings and Map Measurements

Soru 422Soru →

A maintenance crew purchases $8$ gallons of epoxy paint for a warehouse floor. They need to pour the paint into smaller trays that each hold exactly $2$ quarts. How many trays can they fill completely?

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Cevap: 16

Cevap

16 trays

First, find the total number of quarts available. Because there are 4 quarts in 1 gallon, 8 gallons is equal to 32 quarts. Next, divide the 32 total quarts by the 2-quart capacity of each tray. This yields exactly 16 filled trays.

Adım Adım Çözüm

1

Convert the total paint volume from gallons to quarts.

32 quarts

The trays are measured in quarts, so the total paint volume must be converted to the same unit. (8 gallons × 4 quarts/gallon = 32 quarts)

2

Divide the total number of quarts by the capacity of a single tray.

16 trays

This determines how many 2-quart portions can be distributed from the 32 quarts of paint. (32 quarts ÷ 2 quarts/tray = 16 trays)

Anahtar Kavram

Converting between standard US customary volume units (gallons to quarts) and dividing by a unit capacity.

Soru 423Soru →

An HVAC technician is installing a straight run of ventilation ductwork that must be exactly $4$ yards and $2$ feet long. The ducting material comes in standard pre-cut sections that are exactly $20$ inches long. The technician connects these sections end-to-end. Once the connected sections exceed the required length, the excess material is cut off from the final section so the ductwork matches the exact required length. How many inches of material will be cut off and discarded from the final section?

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

12 inches

First, convert the total required length into inches. Since

1

yard equals

3

feet,

4

yards is

12

feet. Adding the extra

2

feet gives a total of

14

feet. Because

1

foot equals

12

inches,

14

feet is

168

inches. Each standard duct section is

20

inches long. Dividing

168

by

20

gives

8

with a remainder of

8

(or

8.4

), meaning

8

full sections provide only

160

inches, which is not enough. A

9^{\text{th}}

section is needed. The total length of

9

uncut sections is

180

inches. To find the amount discarded, subtract the required length from the total material length:

180 - 168 = 12

inches.

Adım Adım Çözüm

1

Convert the required measurement from yards and feet into a single unit of inches.

168 inches

Standardizing the units makes it possible to compare the required length directly with the 20-inch section length.

2

Determine the number of 20-inch sections needed by dividing the total required length by the length of one section.

8.4 sections, which rounds up to 9 sections.

The technician must use whole sections and cut the final one, so we must round up to the next whole number.

3

Calculate the total length of the 9 full sections before any cutting.

180 inches

This represents the total raw material used before the final piece is trimmed to fit.

4

Subtract the exact required length from the total raw material length.

12 inches

The difference between the total material length and the required length is the excess that must be cut off and discarded.

Anahtar Kavram

US Customary Linear Measurements

Soru 424Soru →

A cylindrical farm silo is built to store corn. The interior of the silo has a radius of $7\text{ feet}$ and a height of $20\text{ feet}$ . Using $\frac{22}{7}$ for $\pi$ , what is the total volume of the silo in cubic feet?

Cevabı ve açıklamayı göster

Cevap: 3080

Cevap

The total volume of the silo is 3080 cubic feet.

The correct answer is calculated by applying the volume formula for a cylinder,

V = \pi r^2 h

. Substituting

7

for the radius and

20

for the height, along with

\frac{22}{7}

for

\pi

, results in

3080\text{ cubic feet}

.

Adım Adım Çözüm

1

Recall the volume formula

V = \pi r^2 h

This is the standard formula required to find the volume of any cylinder.

2

Substitute the given values

V = \frac{22}{7} \times (7)^2 \times 20

We plug in

r = 7

,

h = 20

, and

\pi = \frac{22}{7}

as provided in the question.

3

Square the radius

V = \frac{22}{7} \times 49 \times 20

Following the order of operations, exponents must be calculated before multiplication.

4

Multiply and simplify

V = 22 \times 7 \times 20 = 3080

Simplifying the fraction

\frac{22}{7} \times 49

leaves

22 \times 7 = 154

. Multiplying

154

by

20

yields

3080

.

Anahtar Kavram

Calculating the volume of a cylinder

Soru 425Soru →

A machinist is fabricating a circular metal part with a diameter of $12$ inches. To allow for bolts, four identical circular holes, each with a radius of $2$ inches, are cut out of the part. What is the area of the remaining metal in square inches? (Use $\pi = 3.14$ )

Cevabı ve açıklamayı göster

Cevap: 62.8

Cevap

62.8

The remaining area is found by subtracting the total area of the four smaller circular holes from the area of the large circular part. The large part has a radius of 6 inches (half of the 12-inch diameter), giving an area of 113.04 square inches. Each of the four holes has a radius of 2 inches, yielding an area of 12.56 square inches per hole, or 50.24 square inches total. Subtracting 50.24 from 113.04 leaves 62.8 square inches.

Adım Adım Çözüm

1

Find the radius of the large circular part.

Radius = 12 / 2 = 6 inches.

The area formula for a circle requires the radius, but the diameter was given.

2

Calculate the total area of the large circular part.

Area = 3.14 * 6^2 = 113.04 square inches.

This represents the total amount of metal before any holes are cut.

3

Calculate the area of one small bolt hole.

Area = 3.14 * 2^2 = 12.56 square inches.

Each hole is a smaller circle removed from the part.

4

Find the total area of all four bolt holes.

Total hole area = 12.56 * 4 = 50.24 square inches.

There are four identical holes that need to be accounted for.

5

Subtract the total hole area from the large part's area.

Remaining area = 113.04 - 50.24 = 62.8 square inches.

Subtracting the removed material gives the final remaining area of the metal part.

Anahtar Kavram

Calculating and subtracting circular areas

Soru 426Soru →

A naval submarine is traveling underwater at a constant speed of $20\text{ feet per second}$ . At this rate, how many miles will the submarine travel in exactly $1\text{ hour}$ and $6\text{ minutes}$ ?

(Note: $1\text{ mile} = 5,280\text{ feet}$ )

Cevabı ve açıklamayı göster

Cevap: 15

Cevap

15

First, the rate is given as 20 feet per second. The total time must be converted entirely to seconds: 1 hour and 6 minutes equals 66 minutes. Multiplying 66 minutes by 60 seconds per minute gives 3,960 seconds. Next, use the formula Distance = Rate × Time to find the distance in feet: 20 × 3,960 = 79,200 feet. Finally, convert this distance into miles by dividing by 5,280. 79,200 ÷ 5,280 = 15 miles.

Adım Adım Çözüm

1

Convert the total travel time into seconds to match the unit of the given speed.

The total time is 3,960 seconds.

Rates and times must share the same time unit before multiplying.

2

Calculate the total distance traveled in feet by multiplying the speed by the time in seconds.

The distance is 79,200 feet.

Distance equals rate multiplied by time (d = r * t).

3

Convert the distance from feet into miles by dividing by 5,280.

The final distance is 15 miles.

The question asks for the final answer in miles, and there are 5,280 feet in one mile.

Anahtar Kavram

Converting between multiple units of time and distance to solve for a missing variable in the distance formula.

Soru 427Soru →

A military logistics facility is upgrading the security fence around a rectangular motor pool. The motor pool is $50$ yards long and $84$ feet wide. The new design requires leaving a $24$ -foot gap for a main vehicle gate and two separate $3$ -foot gaps for pedestrian access. The security fencing is purchased in pre-assembled panels that are $72$ inches long each. If each panel costs $\$120$ , what is the total cost of the fencing panels needed to enclose the motor pool?

Cevabı ve açıklamayı göster

Cevap: 8760

Cevap

8760 dollars

The correct calculation requires converting all linear measurements to a common unit (feet), calculating the perimeter of the rectangle, subtracting the required gaps for the gates, dividing the remaining length by the panel length to find the total number of panels, and finally multiplying by the cost per panel.

Adım Adım Çözüm

1

Convert yards and inches to feet.

Length is 150 feet; panel length is 6 feet.

To ensure consistency in perimeter and material calculations before determining the number of panels.

2

Calculate the full perimeter of the rectangular motor pool.

468 feet.

To find the total boundary length before accounting for the gaps left for gates.

3

Subtract the total width of the gate gaps from the full perimeter.

438 feet.

Because fencing panels are not installed where the vehicle and pedestrian gates are located.

4

Divide the required fencing length by the length of a single panel.

73 panels.

To find how many discrete 6-foot sections make up the 438-foot fence line.

5

Multiply the number of panels by the cost per panel.

$8,760.

To find the final total price of purchasing the required materials.

Anahtar Kavram

Calculating perimeter with unit conversions and subtracting gaps to find total material cost.

Tahmini Süre:2m 0s

Soru 428Soru →

A builder uses a 15-foot diagonal support beam to brace a vertical wall. If the base of the beam rests on the flat floor exactly 9 feet away from the bottom of the wall, at what height on the wall, in feet, does the top of the beam attach?

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

12

The physical scenario forms a right triangle where the hypotenuse (the beam) measures 15 feet and one leg (along the floor) measures 9 feet. By using the Pythagorean theorem (

a^2 + b^2 = c^2

), we can find the missing leg by solving

9^2 + b^2 = 15^2

. This simplifies to

81 + b^2 = 225

, which means

b^2 = 144

. Taking the square root of 144 gives a wall height of 12 feet.

Adım Adım Çözüm

1

Identify the parts of the right triangle.

Hypotenuse

c = 15

feet, base leg

a = 9

feet, vertical leg

b

is unknown.

The beam forms the hypotenuse opposite the right angle made by the intersection of the vertical wall and flat floor.

2

Apply the Pythagorean theorem.

9^2 + b^2 = 15^2

The Pythagorean theorem (

a^2 + b^2 = c^2

) relates the lengths of the legs of a right triangle to its hypotenuse.

3

Square the known values.

81 + b^2 = 225

To solve for the unknown leg

b

, we must first evaluate the squared terms.

4

Isolate the unknown squared variable.

b^2 = 225 - 81 = 144

Subtracting 81 from both sides leaves

b^2

by itself.

5

Take the square root to find the height.

b = \sqrt{144} = 12

Taking the square root of

b^2

gives the actual length of the wall height.

Anahtar Kavram

Using the Pythagorean theorem to find the missing leg of a right triangle.

Soru 429Soru →

A local radio station broadcasts its signal in a circular area with a radius of $40$ miles. The station upgrades its transmitter, which increases the broadcasting radius to $50$ miles. How many additional square miles of coverage does the upgraded transmitter provide? (Use $\pi = 3.14$ )

Cevabı ve açıklamayı göster

Cevap: 2826

Cevap

2826 square miles

The additional coverage is represented geometrically by the area of the ring (annulus) formed between the two circular boundaries. This is found by calculating both areas and subtracting the original area (

3.14 \times 40^2 = 5024

) from the new area (

3.14 \times 50^2 = 7850

), resulting in

2826

square miles of extra coverage.

Adım Adım Çözüm

1

Calculate the original coverage area.

A_{original} = 3.14 \times 40^2 = 3.14 \times 1600 = 5024

square miles

We must determine the initial broadcast area before the upgrade.

2

Calculate the new coverage area.

A_{new} = 3.14 \times 50^2 = 3.14 \times 2500 = 7850

square miles

We need the total broadcast area provided by the new transmitter.

3

Calculate the additional coverage area by finding the difference.

7850 - 5024 = 2826

square miles

The additional area is the exact difference between the new area and the original area.

Anahtar Kavram

Calculating the difference between two circular areas (area of an annulus).

Alternatif Yöntem

Instead of calculating both areas separately, you can factor the expression for the difference in area:

\Delta A = \pi(R^2 - r^2) = 3.14 \times (50^2 - 40^2) = 3.14 \times (2500 - 1600) = 3.14 \times 900 = 2826

.

Tahmini Süre:1m 30s

Soru 430Soru →

A pharmacist is filling $5$ identical prescriptions for a liquid medication. If each prescription requires $120$ milliliters of the medication, how many liters of medication are dispensed in total?

Cevabı ve açıklamayı göster

Cevap: 0.6

Cevap

0.6 Liters

To find the total amount of medication, first multiply the

5

prescriptions by the

120

milliliters needed for each, which equals

600

milliliters. Because the question asks for the answer in liters, and there are

1000

milliliters in

1

liter, divide the

600

milliliters by

1000

. This gives the final answer of

0.6

liters.

Adım Adım Çözüm

1

Calculate the total required volume in milliliters.

600

mL

Since there are

5

prescriptions and each needs

120

milliliters, multiplying them gives the total amount of medication in the initial unit.

2

Convert the total volume from milliliters to liters.

0.6

Liters

The prefix 'milli-' means one-thousandth. To convert from a smaller unit (milliliters) to a larger base unit (liters), divide by

1000

.

Anahtar Kavram

Multi-step metric system conversions between milli-prefixed units and base units.

Soru 431Soru →

A rectangular fuel holding tank at an aviation depot is $15$ feet long and $10$ feet wide. The tank currently holds $900$ cubic feet of aviation fuel, which fills it to exactly half of its total capacity. What is the total interior height of the tank, in feet?

Cevabı ve açıklamayı göster

Cevap: 12

Cevap

The total interior height of the tank is

12

feet.

By first finding the base area (

15 \times 10 = 150

sq ft), we can determine how high

900

cubic feet of fuel reaches by dividing the volume by the area (

900 \div 150 = 6

feet). Because the tank is half full, the

6

-foot depth is exactly half of the tank's total height, making the total height

12

feet.

Adım Adım Çözüm

1

Calculate the area of the rectangular base of the tank.

15 \text{ ft} \times 10 \text{ ft} = 150 \text{ sq ft}

The volume of a rectangular prism is the product of its base area and height. Finding the base area is the first step to isolating the height.

2

Calculate the current depth of the aviation fuel.

900 \text{ cu ft} \div 150 \text{ sq ft} = 6 \text{ ft}

Dividing the current volume of the fuel by the base area of the tank yields the height (depth) of the liquid currently inside.

3

Calculate the total interior height of the tank.

6 \text{ ft} \times 2 = 12 \text{ ft}

The problem states the tank is exactly half full, meaning the total interior height is twice the depth of the current fuel level.

Anahtar Kavram

Calculating a missing dimension of a rectangular prism using volume and partial capacity

Soru 432Soru →

A metal fabricator starts with a single steel rod that measures exactly $4$ yards and $2$ feet in length. From this rod, they cut $7$ identical segments, each measuring exactly $1$ foot and $5$ inches long. Assuming no material is lost during the cutting process, how many inches of the steel rod remain?

Cevabı ve açıklamayı göster

Cevap: 49

Cevap

49 inches

The correct answer is found by converting all lengths into inches (

4

yards

= 144

in,

2

feet

= 24

in, Total

= 168

in), finding the total length of the cut pieces (

7 \times 17

in

= 119

in), and subtracting the cuts from the total (

168 - 119 = 49

inches).

Adım Adım Çözüm

1

Convert the total initial length of the steel rod into inches.

4

yards

= 144

inches;

2

feet

= 24

inches. Total

= 168

inches.

Converting to the smallest unit (inches) at the beginning prevents errors when subtracting later.

2

Convert the length of a single cut segment into inches.

1

foot

= 12

inches;

12 + 5 = 17

inches per segment.

The length of each cut segment must be in the same base unit as the total rod.

3

Calculate the total length of steel used for all

7

segments.

7 \times 17

inches

= 119

inches.

This determines the total amount of material that will be removed from the original rod.

4

Subtract the total used length from the initial rod length.

168

inches

- 119

inches

= 49

inches.

Subtracting the removed material from the starting material gives the final remaining length.

Anahtar Kavram

Converting multi-unit US Customary linear measurements to a common base unit to perform arithmetic operations.

Soru 433Soru →

A facility management team is filling a newly constructed rectangular water holding tank for the base fire department. The tank's interior measures $30$ feet long, $15$ feet wide, and $10$ feet deep. For safety regulations, the tank must only be filled to $80\%$ of its total capacity. If the water pump delivers $600$ cubic feet of water per hour, how many hours will it take to reach the required fill level?

Cevabı ve açıklamayı göster

Cevap: 6

Cevap

6

The total volume of the tank is

30 \times 15 \times 10 = 4500

cubic feet. Because it must only be filled to

80\%

capacity, the required volume of water is

4500 \times 0.80 = 3600

cubic feet. At a pumping rate of

600

cubic feet per hour, the time needed to reach this level is

3600 \div 600 = 6

hours.

Adım Adım Çözüm

1

Calculate the total volume of the holding tank.

Total Volume = 30 × 15 × 10 = 4500 cubic feet.

The volume of a rectangular prism is found using the formula V = length × width × height.

2

Calculate 80% of the total capacity.

Target Volume = 4500 × 0.80 = 3600 cubic feet.

Safety regulations require the tank to be filled to only 80% of its full capacity.

3

Determine the time required to pump the target volume.

Time = 3600 ÷ 600 = 6 hours.

Time is equal to total volume divided by the rate of flow.

Anahtar Kavram

Calculating rectangular volume, finding a percentage of a total, and applying flow rates to find time.

Alternatif Yöntem

Instead of finding the total volume first, you can find the target depth. 80% of the 10-foot depth is 8 feet. The target volume is then calculated using this adjusted depth: 30 × 15 × 8 = 3600 cubic feet. Divide this by 600 to get 6 hours.

Tahmini Süre:1m 30s

Soru 434Soru →

A volunteer group is installing a wooden fence around a rectangular community garden. The garden measures $30$ feet in length and $18$ feet in width. How many feet of fencing are needed to completely enclose the garden?

Cevabı ve açıklamayı göster

Cevap: 96

Cevap

96

The amount of fencing needed to completely enclose a rectangular space is equal to the perimeter of that space. The formula for the perimeter of a rectangle is

P = 2 \times (L + W)

. By substituting the given length (

30

feet) and width (

18

feet), the perimeter is

2 \times (30 + 18) = 2 \times 48 = 96

feet.

Adım Adım Çözüm

1

Identify the formula for the perimeter of a rectangle.

P = 2 \times (\text{Length} + \text{Width})

The total fencing needed to completely enclose a rectangular area is equal to its perimeter.

2

Substitute the given dimensions into the formula.

P = 2 \times (30 + 18) = 2 \times 48 = 96

This calculates the total linear feet of the boundary for a garden with a length of 30 feet and a width of 18 feet.

Anahtar Kavram

The total length of fencing required to enclose a rectangular area is equal to its perimeter, calculated as

2 \times (\text{length} + \text{width})

.

Soru 435Soru →

A rancher is building a fence around a rectangular grazing pasture. The pasture is $140$ feet long and $70$ feet wide. If the rancher needs to leave a $10$ -foot wide opening for a gate, how many total feet of fencing material will be required?

Cevabı ve açıklamayı göster

Cevap: 410

Cevap

410 feet

To find the total amount of fencing required, you first determine the perimeter of the rectangle, which is

140 + 140 + 70 + 70 = 420

feet. Because there is a

10

-foot gate that does not require fencing, you subtract

10

from the total perimeter, leaving

410

feet.

Adım Adım Çözüm

1

Calculate the total perimeter of the rectangular pasture.

2 \times (140 + 70) = 420

feet.

The fence runs along the entire outer boundary of the pasture, which requires finding the perimeter of the rectangle.

2

Subtract the gate opening from the total perimeter.

420 - 10 = 410

feet.

The

10

-foot opening for the gate does not use fencing material, so it must be subtracted from the total.

Anahtar Kavram

Calculating perimeter of a rectangle and adjusting for gaps or openings.

Soru 436Soru →

A combat engineer platoon is constructing a defensive barrier. They use $15$ sandbags to reinforce a specific section. If each filled sandbag weighs exactly $42$ pounds and $12$ ounces, what is the total weight of the sandbags used for this section, in pounds?

Cevabı ve açıklamayı göster

Cevap: 641.25

Cevap

641.25

The correct calculation requires first establishing the exact weight of a single sandbag in pounds. Because there are

16

ounces in

1

pound,

12

ounces converts to

0.75

pounds (

12 \div 16

). Adding this to the base

42

pounds yields

42.75

pounds per sandbag. Multiplying this decimal weight by the

15

sandbags results in exactly

641.25

pounds.

Adım Adım Çözüm

1

Convert the ounce portion of the sandbag weight into pounds.

12 \text{ oz} \div 16 \text{ oz/lb} = 0.75 \text{ lbs}

To perform accurate arithmetic operations in a single unit, the mixed US Customary unit must be standardized into pounds.

2

Calculate the total weight of one sandbag in pounds.

42 \text{ lbs} + 0.75 \text{ lbs} = 42.75 \text{ lbs}

Combines the converted ounce value with the existing pound value to find the exact decimal weight of a single unit.

3

Multiply the single sandbag weight by the total number of sandbags.

42.75 \text{ lbs} \times 15 = 641.25 \text{ lbs}

Finds the aggregate weight for all

15

sandbags used in the section.

Anahtar Kavram

Converting mixed US Customary weight units (pounds and ounces) to a single decimal unit and calculating aggregate weight.

Soru 437Soru →

A city construction crew is installing a new cylindrical concrete drainage pipe. The interior of the pipe has a diameter of $10\text{ feet}$ and a length of $100\text{ feet}$ . Using $3.14$ for $\pi$ , what is the maximum volume of water the pipe can hold when completely full, in cubic feet?

Cevabı ve açıklamayı göster

Cevap: 7850

Cevap

The pipe can hold a maximum volume of 7,850 cubic feet.

The volume of a cylinder is found by multiplying the area of its circular base by its height or length (

V = \pi r^2 h

). First, convert the given diameter of

10\text{ feet}

to a radius by dividing by

2

, yielding a radius of

5\text{ feet}

. Next, square the radius to get

25

. Multiply this by the length (

100\text{ feet}

) and the approximate value of

\pi

(

3.14

).

3.14 \times 25 \times 100 = 7,850\text{ cubic feet}

.

Adım Adım Çözüm

1

Find the radius of the pipe.

r = 10 \div 2 = 5\text{ feet}

The volume formula for a cylinder requires the radius, which is half of the diameter.

2

Apply the volume formula for a cylinder.

V = \pi \times r^2 \times h

To find the capacity of the cylindrical pipe, we must calculate its three-dimensional space, which is volume.

3

Substitute the known values into the formula.

V = 3.14 \times 5^2 \times 100

We use the given values: radius

5\text{ feet}

, height (or length)

100\text{ feet}

, and

\pi \approx 3.14

.

4

Calculate the final volume.

V = 3.14 \times 25 \times 100 = 3.14 \times 2500 = 7850

Squaring the radius gives

25

. Multiplying by

100

and

3.14

gives the total volume in cubic feet.

Anahtar Kavram

Calculating the volume of a cylinder using the formula

V = \pi r^2 h

, ensuring the given diameter is converted to a radius before performing calculations.

Soru 438Soru →

During standard patrol missions, the Los Angeles-class fast attack submarine operates with a complement of 143 personnel. While submerged, the onboard atmospheric revitalization system maintains oxygen levels for up to 90 days between port calls. Routine maintenance schedules require technicians to inspect the main seawater cooling valves every 45 days. According to the passage, how many days can the onboard atmospheric revitalization system maintain oxygen levels while submerged?

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Cevap: 90

Cevap

The onboard atmospheric revitalization system can maintain oxygen levels for 90 days while submerged.

The passage explicitly states that while submerged, the atmospheric revitalization system maintains oxygen levels for up to 90 days between port calls.

Adım Adım Çözüm

1

Locate the sentence addressing the atmospheric revitalization system and oxygen maintenance.

Found the statement: 'While submerged, the onboard atmospheric revitalization system maintains oxygen levels for up to 90 days between port calls.'

Direct retrieval of the relevant factual statement is required to extract the requested quantity accurately.

2

Extract the numerical value tied directly to the submerged oxygen duration and verify it against adjacent figures.

The target duration is 90 days.

Differentiates the oxygen duration (90 days) from the inspection interval (45 days) and the crew size (143 personnel).

Anahtar Kavram

Direct quantitative detail extraction from informational text

Tahmini Süre:45s

Soru 439Soru →

A hotel maintenance team is installing a new cylindrical hot water heater. The interior of the heater has a diameter of $4\text{ feet}$ and a height of $7\text{ feet}$ . Using $\frac{22}{7}$ for $\pi$ , how many minutes will it take to completely fill the empty heater if water flows in at a constant rate of $4\text{ cubic feet}$ per minute?

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Cevap: 22

Cevap

It will take 22 minutes to completely fill the hot water heater.

The correct answer is found by first calculating the volume of the cylindrical heater using the formula

V = \pi r^2 h

. Given the diameter of

4\text{ feet}

, the radius is

2\text{ feet}

. Substituting the given values:

V = \frac{22}{7} \times 2^2 \times 7 = 88\text{ cubic feet}

. Dividing this total volume by the fill rate of

4\text{ cubic feet}

per minute gives the total time:

88 \div 4 = 22\text{ minutes}

.

Adım Adım Çözüm

1

Determine the radius of the cylindrical heater.

Radius =

2\text{ feet}

The volume formula requires the radius, which is half of the given diameter (

4\text{ feet}

).

2

Calculate the total volume of the cylinder.

Volume =

88\text{ cubic feet}

Using the formula

V = \pi r^2 h

with

r = 2

,

h = 7

, and

\pi = \frac{22}{7}

, we get

V = \frac{22}{7} \times 2^2 \times 7 = 88

.

3

Calculate the time required to fill the heater.

Time =

22\text{ minutes}

Dividing the total volume (

88\text{ cubic feet}

) by the flow rate (

4\text{ cubic feet}

per minute) gives the required time.

Anahtar Kavram

Cylindrical Volume Applications

Soru 440Soru →

A cargo master is preparing an air drop bundle. The bundle contains $64$ identical medical supply boxes. Each box weighs exactly $6$ pounds and $4$ ounces. The parachute and rigging equipment add an additional $125$ pounds to the total load. What is the total combined weight, in pounds, of the fully rigged bundle?

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Cevap: 525

Cevap

525

The correct answer is found by first converting the weight of each medical box entirely into pounds. Since there are

16

ounces in a pound,

4

ounces is equal to

\frac{4}{16}

or

0.25

pounds, making each box

6.25

pounds. Multiplying this weight by the

64

boxes gives a total medical supply weight of

400

pounds. Adding the

125

pounds for the parachute and rigging equipment gives a final total weight of

525

pounds.

Adım Adım Çözüm

1

Convert the fractional ounces into pounds.

4 ounces = 0.25 pounds, making each box 6.25 pounds.

To standardize the unit of measurement to pounds before calculating the total weight.

2

Calculate the total weight of all medical boxes.

64 boxes × 6.25 lbs/box = 400 lbs.

To find the aggregate weight of the payload.

3

Add the weight of the rigging equipment.

400 lbs + 125 lbs = 525 lbs.

The question asks for the total combined weight of the fully rigged bundle.

Anahtar Kavram

US Customary Weight Measurement Conversions

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