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Difficulty: MediumRectangular Volume and Container Capacity

A rectangular training pool at a military base is 4040 feet long and 2525 feet wide. It is initially filled with water to a uniform depth of 88 feet. If 1,5001,500 cubic feet of water is pumped out of the pool, what is the new depth of the water, in feet?

Answer: 6.5 feet

Answer

6.5
The pool's base has an area of 40×25=1,00040 \times 25 = 1,000 square feet. When 1,5001,500 cubic feet of water is removed, the water level drops by 1,500÷1,000=1.51,500 \div 1,000 = 1.5 feet. Subtracting this drop from the initial depth of 88 feet gives a new depth of 6.56.5 feet. Alternatively, finding the original volume (8,0008,000 cubic feet), subtracting the removed water (6,5006,500 cubic feet), and dividing by the area (1,0001,000 square feet) also yields 6.56.5 feet.

Step-by-Step Solution

1
Calculate the base area of the rectangular pool.
1,0001,000 square feet
The base area is needed to determine how changes in volume affect the depth of the water. Area = length ×\times width = 40×25=1,00040 \times 25 = 1,000.
2
Determine the change in the water depth.
The depth drops by 1.51.5 feet.
Dividing the removed volume by the base area gives the vertical drop in water level. 1,500÷1,000=1.51,500 \div 1,000 = 1.5.
3
Calculate the new depth.
6.56.5 feet
Subtract the drop in water level from the initial depth. 8−1.5=6.58 - 1.5 = 6.5.

Key Concept

Calculating changes in the depth of a rectangular volume when a specific amount of capacity is removed.
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Topics

Rectangular Volume and Container Capacity

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