Measurement and Unit Conversions Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) — Sayfa 4

Soru 61Soru →

A military supply officer is inventorying emergency drinking water supplies stored in four different transport containers. To properly balance the cargo load for an upcoming transport flight, the officer needs to evaluate their relative capacities. Arrange the following containers from least to greatest volume of water.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The correct sequence from least to greatest volume is Container C, Container D, Container A, and Container B.

To accurately compare the volumes, each measurement must be standardized to a common unit, such as liters. Container C converts to

450

liters (

450,000 \div 1,000

). Container D converts to

465

liters (

46,500 \div 100

). Container A converts to

480

liters (

0.48 \times 1,000

). Container B is already given as

490

liters. Arranging these converted values from least to greatest yields Container C, Container D, Container A, and Container B.

Adım Adım Çözüm

1

Convert the volume of Container A to liters.

0.48 \text{ kL} \times 1,000 = 480 \text{ L}

The prefix kilo- means 1,000. Multiplying kiloliters by 1,000 converts the measurement to the base unit of liters.

2

Convert the volume of Container C to liters.

450,000 \text{ mL} \div 1,000 = 450 \text{ L}

The prefix milli- means one-thousandth. Dividing milliliters by 1,000 converts the measurement to liters.

3

Convert the volume of Container D to liters.

46,500 \text{ cL} \div 100 = 465 \text{ L}

The prefix centi- means one-hundredth. Dividing centiliters by 100 converts the measurement to liters.

4

Compare the standardized values to establish the final order.

450 \text{ L} < 465 \text{ L} < 480 \text{ L} < 490 \text{ L}

Ordering the converted numerical values directly dictates the arrangement from least to greatest capacity.

Anahtar Kavram

Converting metric capacity units (kiloliters, liters, centiliters, milliliters) to a common base unit to compare magnitudes.

Soru 62Soru →

A wire manufacturing facility operates $40$ extrusion machines simultaneously. Each machine produces $15$ centimeters of copper wire per second. How many kilometers of copper wire do all $40$ machines produce combined in exactly one hour?

0.36

2,160

21.6

21,600

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Cevap: $21.6$

Cevap

The machines produce a combined total of

21.6

kilometers of copper wire in one hour.

First, find the facility's total production per second by multiplying

40

machines by

15

cm, yielding

600

cm/sec. Next, multiply by

3,600

(the number of seconds in one hour) to find the hourly production in centimeters, which equals

2,160,000

cm. Finally, convert centimeters to kilometers by dividing by

100,000

(

100 \text{ cm} = 1 \text{ m}

and

1,000 \text{ m} = 1 \text{ km}

), resulting in

21.6

kilometers.

Adım Adım Çözüm

1

Calculate the total length of wire produced per second by all machines combined.

40 \times 15 = 600

centimeters per second.

This establishes the facility's baseline production rate before factoring in a longer duration.

2

Scale the production rate from seconds to hours.

600 \times 3,600 = 2,160,000

centimeters per hour.

There are

60

seconds in a minute and

60

minutes in an hour, meaning there are

3,600

seconds in exactly one hour.

3

Convert the total length from centimeters to kilometers.

2,160,000 \div 100,000 = 21.6

kilometers.

Since there are

100

centimeters in a meter and

1,000

meters in a kilometer, the total conversion factor is

100,000

centimeters per kilometer.

Anahtar Kavram

Multi-step metric prefix conversions involving time rates and combined totals.

Soru 63Soru →

A military transport aircraft has a maximum cargo capacity of $15,000 \text{ kilograms}$ . The aircraft is currently loaded with $19,800 \text{ pounds}$ of equipment. If $1 \text{ kilogram}$ is equal to $2.2 \text{ pounds}$ , how much additional cargo, in kilograms, can the aircraft carry?

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Cevap: 6000

Cevap

6000

The remaining capacity is found by first standardizing all measurements to kilograms (

19,800 \text{ pounds} \div 2.2 = 9,000 \text{ kilograms}

), and then subtracting this from the total allowance (

15,000 \text{ kg} - 9,000 \text{ kg} = 6,000 \text{ kg}

).

Adım Adım Çözüm

1

Convert the current load from pounds to kilograms.

19,800 \div 2.2 = 9,000 \text{ kg}

Since the maximum capacity is given in kilograms and the final answer must be in kilograms, the current load must be converted to the metric system.

2

Subtract the current load from the maximum cargo capacity.

15,000 - 9,000 = 6,000 \text{ kg}

Subtracting the weight already on board from the maximum allowable weight gives the remaining available capacity.

Anahtar Kavram

Converting units between the US Customary and metric systems using a given conversion factor, followed by basic arithmetic subtraction.

Soru 64Soru →

A military engineering unit is laying communication cable between two outposts. The total required distance for the connection is $4.5 \text{ miles}$ . The supply depot issues this specific cable in standard spools containing $500 \text{ meters}$ of cable each. If $1 \text{ mile}$ is approximately equal to $1.6 \text{ kilometers}$ , what is the minimum number of spools the unit must request to ensure they have enough cable to cover the entire distance?

6

9

15

144

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Cevap: 15

Cevap

15

To find the total number of spools needed, first unify the units of measurement. Convert 4.5 miles into kilometers by multiplying by 1.6, yielding 7.2 kilometers. Since the spools are measured in meters, convert 7.2 kilometers into meters by multiplying by 1,000, which equals 7,200 meters. Next, divide the 7,200-meter total distance by the 500 meters contained on each spool, resulting in 14.4 spools. Because a fraction of a spool cannot be requested and the full distance must be covered, the number must be rounded up to the nearest whole spool, making 15 the correct amount to request.

Adım Adım Çözüm

1

Convert the total distance from miles to kilometers using the given conversion factor.

4.5 \text{ miles} \times 1.6 \text{ km/mile} = 7.2 \text{ kilometers}

To standardize the units, the distance must first be brought into the metric system where the spool length is measured.

2

Convert the distance from kilometers to meters.

7.2 \text{ km} \times 1,000 \text{ m/km} = 7,200 \text{ meters}

The spools are measured in meters, so the total distance required must match this unit.

3

Determine the exact number of spools required by dividing the total meters by the meters per spool.

7,200 \text{ meters} \div 500 \text{ meters/spool} = 14.4 \text{ spools}

This finds how many 500-meter increments are needed to cover the 7,200-meter distance.

4

Round up to the nearest whole number.

15 \text{ spools}

Since the unit cannot be issued a fraction of a spool and 14 spools would leave them short of the required distance, they must request the next whole number.

Anahtar Kavram

Converting across measurement systems (US Customary to Metric) and solving practical constraints using the ceiling function.

Soru 65Soru →

A military supply officer is preparing cargo for an allied joint exercise. Match the following US Customary measurements to their approximate Metric equivalents based on standard conversion rates ( $1 \text{ inch} = 2.54 \text{ cm}$ , $1 \text{ kg} \approx 2.2 \text{ lbs}$ , $1 \text{ mile} \approx 1.6 \text{ km}$ , $1 \text{ gallon} \approx 3.78 \text{ L}$ ).

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

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Cevap

The correct pairings are:

10 \text{ inches}

matches with

25.4 \text{ centimeters}

,

5 \text{ miles}

matches with

8 \text{ kilometers}

,

110 \text{ pounds}

matches with

50 \text{ kilograms}

, and

10 \text{ gallons}

matches with

37.8 \text{ liters}

.

Each measurement is paired with its metric equivalent by correctly applying the given conversion factors. Multiplying is used to convert inches to centimeters, miles to kilometers, and gallons to liters. Dividing is required to convert pounds to kilograms.

Adım Adım Çözüm

1

Identify the conversion factors provided in the prompt.

1 \text{ inch} = 2.54 \text{ cm}

,

1 \text{ kg} = 2.2 \text{ lbs}

,

1 \text{ mile} = 1.6 \text{ km}

,

1 \text{ gallon} = 3.78 \text{ L}

These rates determine whether to multiply or divide.

2

Convert the clearance height from inches to centimeters.

10 \times 2.54 = 25.4 \text{ cm}

Multiplying by the factor converts US standard length to metric.

3

Convert the marching distance from miles to kilometers.

5 \times 1.6 = 8 \text{ km}

Multiplying miles by

1.6

yields the correct distance in kilometers.

4

Convert the crate weight from pounds to kilograms.

110 \div 2.2 = 50 \text{ kg}

Since

1 \text{ kg}

is

2.2 \text{ lbs}

, dividing the total pounds by

2.2

gives the number of kilograms.

5

Convert the fuel capacity from gallons to liters.

10 \times 3.78 = 37.8 \text{ L}

Multiplying gallons by the conversion factor

3.78

yields the volume in liters.

Anahtar Kavram

Inter-System Unit Conversions

Soru 66Soru →

A naval architect creates a scale drawing for a new submarine. The drawing uses a scale of $\frac{3}{16}\text{ inch} = 15\text{ feet}$ . If the pressure hull measures $4\frac{1}{8}\text{ inches}$ long on the drawing, what is the actual length, in feet, of the pressure hull?

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Cevap: 330

Cevap

330

The scale establishes that every inch on the drawing represents

80

actual feet (

15 \div \frac{3}{16} = 80

). Multiplying the drawing length of

4\frac{1}{8}

inches (or

\frac{33}{8}

inches) by

80

feet per inch yields the correct actual length of

330

feet.

Adım Adım Çözüm

1

Find the unit rate for

1\text{ inch}

of the drawing.

15 \div \frac{3}{16} = 15 \times \frac{16}{3} = 5 \times 16 = 80\text{ feet}

per inch.

Establishing a unit rate simplifies finding actual dimensions for any measurement on the scale drawing.

2

Convert the drawing measurement from a mixed number to an improper fraction.

4\frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8}\text{ inches}

.

Improper fractions are required to properly multiply the scale factor with the drawing measurement.

3

Calculate the actual length by multiplying the map measurement by the unit rate.

\frac{33}{8} \times 80 = 33 \times 10 = 330\text{ feet}

.

Multiplying the measurement on the drawing by the actual distance per inch yields the total actual distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Soru 67Soru →

A search and rescue grid map uses a scale of $\frac{2}{3}\text{ inch} = 10\text{ miles}$ . If a distress beacon is located $60\text{ miles}$ away from the rescue station, what is the distance between these two points on the map in inches?

4

6

9

40

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Cevap: $4$

Cevap

The distance on the map is

4

inches.

To find the map distance, first determine the scale multiplier by dividing the total actual distance by the reference distance in the scale (

60 \div 10 = 6

). Next, multiply this factor by the scale measurement on the map (

6 \times \frac{2}{3} = \frac{12}{3} = 4

). Thus, the distance on the map is exactly

4

inches.

Adım Adım Çözüm

1

Determine how many

10

-mile units fit into the total actual distance of

60

miles.

60 \div 10 = 6

units.

This establishes the scale multiplier, telling us how many times we need to apply the map's specified scale distance.

2

Multiply the scale multiplier by the map's fractional measurement.

6 \times \frac{2}{3} = \frac{12}{3} = 4

inches.

Because each

10

-mile unit represents

\frac{2}{3}

of an inch on the map, multiplying them gives the total map distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Soru 68Soru →

A logistics coordinator is planning a delivery route using a regional highway map. The map's legend indicates a scale of $0.4\text{ inches} = 15\text{ miles}$ . If the distance between the distribution center and the final delivery point measures $6.2\text{ inches}$ on the map, what is the actual driving distance between the two locations?

23.25\text{ miles}

37.2\text{ miles}

93\text{ miles}

232.5\text{ miles}

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Cevap: $232.5\text{ miles}$

Cevap

The actual driving distance is

232.5\text{ miles}

.

The correct actual distance is

232.5\text{ miles}

. To solve this, find the number of

0.4

-inch units in

6.2\text{ inches}

by dividing:

6.2 \div 0.4 = 15.5

. Then, multiply this factor by the

15\text{ miles}

that each unit represents:

15.5 \times 15 = 232.5\text{ miles}

. Alternatively, finding the unit rate of

37.5\text{ miles per inch}

(

15 \div 0.4

) and multiplying by

6.2\text{ inches}

yields the same correct result.

Adım Adım Çözüm

1

Determine the unit scale (actual miles per inch on the map).

15 \div 0.4 = 37.5\text{ miles per inch}

This establishes a baseline multiplier to convert any map measurement into real-world miles.

2

Calculate the actual driving distance.

6.2 \times 37.5 = 232.5\text{ miles}

Scaling up the measured map distance by the unit rate yields the total actual distance.

Anahtar Kavram

Scale Drawings and Map Measurements

Tahmini Süre:1m 30s

Soru 69Soru →

Calculate the actual length of the property line based on the given scale and enter the exact numerical value.

Aşağıdaki boşlukları doldurun

A city surveyor is examining a property deed map that uses a scale of

1\frac{1}{2}\text{ inches} = 40\text{ feet}

. If the eastern boundary line measures

5\frac{1}{4}\text{ inches}

on this map, the actual length of the boundary line is feet.

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Cevap

140

The correct answer is found by setting up a direct proportion based on the scale:

\frac{1.5\text{ inches}}{40\text{ feet}} = \frac{5.25\text{ inches}}{x\text{ feet}}

. Cross-multiplying gives

1.5x = 210

, and dividing by

1.5

gives an actual length of

140

feet.

Adım Adım Çözüm

1

Convert the mixed fractions into decimals for easier algebraic calculation.

The map scale is

1.5\text{ inches} = 40\text{ feet}

. The measured boundary is

5.25\text{ inches}

.

Working with decimals simplifies the process of setting up and solving a proportion.

2

Set up a direct proportion comparing the map distance to the actual distance.

\frac{1.5\text{ inches}}{40\text{ feet}} = \frac{5.25\text{ inches}}{x\text{ feet}}

A map's scale establishes a consistent ratio between the dimensions on the drawing and the true physical dimensions.

3

Cross-multiply the terms to isolate the unknown variable

x

.

1.5x = 40 \times 5.25

Cross-multiplication transforms the proportion into a linear equation that is easy to solve.

4

Multiply the values on the right side of the equation.

40 \times 5.25 = 210

Simplifying the right side to

210

leaves a basic one-step algebraic equation:

1.5x = 210

.

5

Divide both sides by

1.5

to solve for

x

.

x = \frac{210}{1.5} = 140

Dividing by the coefficient isolates

x

, revealing the actual length of the boundary line in feet.

Anahtar Kavram

Using proportional reasoning and cross-multiplication to convert map measurements to real-world distances.

Measurement and Unit Conversions

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