The pool can hold 65.84 ft³ of water
Explanation:
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
[tex]\frac{11}{1+\sqrt{2} } = a^2[/tex]
a² = [tex]\frac{11}{2.42}[/tex]
a² = 4.55
a = 2.132 ft
Side length of the octagon is 2.132 ft
We know:
Volume of octagon = [tex]2(1+\sqrt{2} ) X (a)^2 X h[/tex]
[tex]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[/tex]
Therefore, the pool can hold 65.84 ft³ of water
