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Joanne has a cylindrical, above ground pool. the depth (height) of the pool is 1/2 of its radius, and the volume is 1570 cubic feet. What is the area of its bottom floor? The diameter of the pool floor must also be at most 22 feet.

Answer :

Answer:

314 ft²

Step-by-step explanation:

Data provided in the question:

Depth (height) of the pool = [tex]\frac{1}{2}[/tex] of its radius

let the radius be 'r' ft

thus,

Depth (height) of the pool, h = [tex]\frac{r}{2}[/tex] ft

Volume of the pool = 1570 ft³

also,

Volume of cylinder = πr²h

thus,

1570 ft³ = πr²h

or

1570 ft³ = [tex]\pi r^2(\frac{r}{2})[/tex]

or

3140 = 3.14 × r³                     [ π = 3.14 ]

or

r³ = 1000 ft³

or

r = 10 ft

Thus,

Area of the bottom surface = πr²

= 3.14 × 10²

= 314 ft²

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