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Ann [662]
3 years ago
14

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 f

eet. What is the area of its bottom floor? The diameter of the pool floor must also be at most 22 feet.
Mathematics
1 answer:
diamong [38]3 years ago
5 0

Answer:

314 ft²

Step-by-step explanation:

Data provided in the question:

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

let the radius be 'r' ft

thus,

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

Volume of the pool = 1570 ft³

also,

Volume of cylinder = πr²h

thus,

1570 ft³ = πr²h

or

1570 ft³ = \pi r^2(\frac{r}{2})

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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