During a base expansion project, civil engineers are preparing a rectangular wooden form t… — Armed Services Vocational Aptitude Battery (ASVAB)

During a base expansion project, civil engineers are preparing a rectangular wooden form to cast a concrete foundation block. The interior of the form measures $12.5$ feet in length, $8$ feet in width, and $36$ inches in depth. If a mixer truck pumps concrete into the form at a constant rate of $20$ cubic feet per minute, how many minutes will it take to fill the form completely?

A
$5$
$15$ Answer
C
$150$
D
$180$

Answer

It will take 15 minutes to completely fill the concrete form.

To find the time it takes to fill the form, first ensure all dimensions are in the same unit. The length and width are in feet, but the depth is in inches. Converting

36

inches to feet yields

3

feet. Next, calculate the total volume of the rectangular form using the formula

V = l \times w \times h

. Multiplying

12.5 \text{ ft} \times 8 \text{ ft} \times 3 \text{ ft}

gives a total volume of

300

cubic feet. Finally, divide this total volume by the pouring rate of

20

cubic feet per minute.

300 \div 20 = 15

minutes.

Step-by-Step Solution

Convert the depth from inches to feet to match the other dimensions and the unit of the flow rate.

36 \text{ inches} \div 12 \text{ inches/foot} = 3 \text{ feet}

Volume calculations require all linear dimensions to be in the same unit before multiplying.

Calculate the total volume of the rectangular form.

12.5 \text{ ft} \times 8 \text{ ft} \times 3 \text{ ft} = 300 \text{ cubic feet}

The capacity of a rectangular container is found by multiplying its length, width, and depth (

V = l \times w \times h

Calculate the time required to fill the form by dividing the total volume by the pumping rate.

300 \text{ cubic feet} \div 20 \text{ cubic feet/minute} = 15 \text{ minutes}

Time equals total volume divided by the rate of flow.

Key Concept

Calculating the volume of a rectangular prism (

V = l \times w \times h

) with proper unit conversions, and using rates to find total time.

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