A city construction crew is installing a new cylindrical concrete drainage pipe. The inter… — Armed Services Vocational Aptitude Battery (ASVAB)

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?

Answer: 7850 cubic feet

Answer

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}

Step-by-Step Solution

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.

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.

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

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.

Key Concept

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.

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