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Jlenok [28]
3 years ago
5

An octagonal swimming pool has a base area of 22 square feet The pool is 3 feet deep How many cubic feet of water can the pool h

old?
Mathematics
1 answer:
LenKa [72]3 years ago
8 0

The pool can hold 65.84 ft³ of water

<u>Explanation:</u>

Given:

Shape of pool = octagonal

Base area of the pool = 22 ft²

Depth of the pool = 3 feet

Volume, V = ?

We know:

Area of octagon = 2 ( 1 + √2) a²

22 ft² = 2 ( 1 + √2 ) a²

\frac{11}{1+\sqrt{2} } = a^2

a² = \frac{11}{2.42}

a² = 4.55

a = 2.132 ft

Side length of the octagon is 2.132 ft

We know:

Volume of octagon = 2(1+\sqrt{2} ) X (a)^2 X h

V = 2(1+\sqrt{2})X (2.132)^2 X 3\\ \\V = 2 ( 2.414) X 4.5454 X 3\\\\V = 65.84 ft^3

Therefore, the pool can hold 65.84 ft³ of water

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