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Difficulty: MediumRectangular Volume and Container Capacity

A facility management team is filling a newly constructed rectangular water holding tank for the base fire department. The tank's interior measures 3030 feet long, 1515 feet wide, and 1010 feet deep. For safety regulations, the tank must only be filled to 80%80\% of its total capacity. If the water pump delivers 600600 cubic feet of water per hour, how many hours will it take to reach the required fill level?

Answer: 6 hours

Answer

6
The total volume of the tank is 30×15×10=450030 \times 15 \times 10 = 4500 cubic feet. Because it must only be filled to 80%80\% capacity, the required volume of water is 4500×0.80=36004500 \times 0.80 = 3600 cubic feet. At a pumping rate of 600600 cubic feet per hour, the time needed to reach this level is 3600÷600=63600 \div 600 = 6 hours.

Step-by-Step Solution

1
Calculate the total volume of the holding tank.
Total Volume = 30 × 15 × 10 = 4500 cubic feet.
The volume of a rectangular prism is found using the formula V = length × width × height.
2
Calculate 80% of the total capacity.
Target Volume = 4500 × 0.80 = 3600 cubic feet.
Safety regulations require the tank to be filled to only 80% of its full capacity.
3
Determine the time required to pump the target volume.
Time = 3600 ÷ 600 = 6 hours.
Time is equal to total volume divided by the rate of flow.

Key Concept

Calculating rectangular volume, finding a percentage of a total, and applying flow rates to find time.

Alternative Method

Instead of finding the total volume first, you can find the target depth. 80% of the 10-foot depth is 8 feet. The target volume is then calculated using this adjusted depth: 30 × 15 × 8 = 3600 cubic feet. Divide this by 600 to get 6 hours.
Estimated Time:1m 30s
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Topics

Rectangular Volume and Container Capacity

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