How to find the volume of a polyhedron

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PSAT Math › How to find the volume of a polyhedron

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Swimming_pool

The above depicts a rectangular swimming pool for an apartment. 80% of the pool is six feet deep, and the remaining part of the pool is four feet deep. How many cubic feet of water does the pool hold?

$9,800 \textrm{ ft}^{3}$

$10,800 \textrm{ ft}^{3}$

$8,750 \textrm{ ft}^{3}$

$9,750 \textrm{ ft}^{3}$

None of the other choices gives the correct answer.

Explanation

The cross-section of the pool is the area of its surface, which is the product of its length and its width:

$50 \times 35 = 1,750$ square feet.

Since 80% of the pool is six feet deep, this portion of the pool holds

$0.80 \times 1,750 \times 6 = 8,400$ cubic feet of water.

Since the remainder of the pool - 20% - is four feet deep, this portion of the pool holds

$0.20 \times 1,750 \times 4 = 1,400$ cubic feet of water.

Add them together: the pool holds

cubic feet of water.

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