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Difficulty: MediumRectangular Volume and Container Capacity

A maintenance crew is installing a new rectangular cooling fluid reservoir for an industrial generator. The interior of the reservoir measures 44 feet long, 33 feet wide, and 1818 inches deep. If the crew fills the empty reservoir at a constant rate of 1.51.5 cubic feet per minute, how many minutes will it take to fill the reservoir completely?

  1. A
    1.2
  2. B
    8
  3. 12Answer
  4. D
    144

Answer

It will take 12 minutes to fill the reservoir completely.
The correct answer is 1212. To determine the fill time, the dimensions must first be unified. Since the flow rate is in cubic feet, 1818 inches must be converted to 1.51.5 feet. The interior volume of the rectangular reservoir is then 4 ft×3 ft×1.5 ft=18 cubic feet4 \text{ ft} \times 3 \text{ ft} \times 1.5 \text{ ft} = 18 \text{ cubic feet}. Dividing this total volume by the filling rate of 1.51.5 cubic feet per minute yields exactly 1212 minutes.

Step-by-Step Solution

1
Convert the depth measurement from inches to feet.
18 inches÷12=1.5 feet18 \text{ inches} \div 12 = 1.5 \text{ feet}.
All dimensions must be in the same unit (feet) because the flow rate is provided in cubic feet per minute.
2
Calculate the total volume of the rectangular reservoir.
4 ft×3 ft×1.5 ft=18 cubic feet4 \text{ ft} \times 3 \text{ ft} \times 1.5 \text{ ft} = 18 \text{ cubic feet}.
The capacity of a rectangular container is found using the volume formula V=l×w×hV = l \times w \times h.
3
Determine the time required to fill the reservoir.
18 cubic feet÷1.5 cubic feet per minute=12 minutes18 \text{ cubic feet} \div 1.5 \text{ cubic feet per minute} = 12 \text{ minutes}.
Time is equal to the total volume divided by the rate of flow.

Key Concept

Calculating rectangular volume with unit conversions and applying rates.
Estimated Time:1m 30s
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Topics

Rectangular Volume and Container Capacity

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