A disaster relief organization is setting up a rectangular emergency water reservoir that … — Armed Services Vocational Aptitude Battery (ASVAB)

A disaster relief organization is setting up a rectangular emergency water reservoir that measures $4$ yards long, $3$ yards wide, and $2$ yards deep. The reservoir is currently filled to $75\%$ of its total capacity. If $1$ cubic foot holds exactly $7.5$ gallons of water, and the water is distributed into standard $3$ -gallon jugs, how many full jugs can be filled?

A
135
1,215Answer
C
3,645
D
10,935

Answer

1,215

The correct answer is found by first calculating the volume in cubic yards (

24

), converting it to cubic feet by multiplying by

27

(

648

), taking

75\%

of that volume (

486

), converting to total gallons by multiplying by

7.5

(

3,645

), and finally dividing by

3

to find the number of jugs (

1,215

Step-by-Step Solution

Calculate the total volume of the reservoir in cubic yards.

4 \times 3 \times 2 = 24 \text{ yd}^3

Multiplying the given length, width, and depth provides the total capacity of the rectangular reservoir.

Convert the volume from cubic yards to cubic feet.

24 \times 27 = 648 \text{ ft}^3

There are 3 feet in a yard, so there are

3^3

, or

27

, cubic feet in one cubic yard.

Calculate the volume of water currently inside the reservoir.

648 \times 0.75 = 486 \text{ ft}^3

The reservoir is filled to

75\%

capacity, so we multiply the total volume by

0.75

Convert the volume of the water into gallons.

486 \times 7.5 = 3,645 \text{ gallons}

Each cubic foot holds

7.5

gallons, so multiplying by this rate gives the total gallons of water available.

Determine the number of full

3

-gallon jugs that can be filled.

3,645 \div 3 = 1,215 \text{ jugs}

Dividing the total gallons of water by the capacity of a single jug gives the number of jugs.

Key Concept

Converting between linear dimensions and capacity, and applying multi-step rate calculations to find unit counts.

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