Question

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? Include equations or inequalities related.

Answer 1

The area of its bottom floor is 314.16 cm²

Explanation:

Joanne has a cylindrical, with volume as 1570 cm³.

Height of the pool is half of the radius of its base.

Let us assume the length of radius is r cm, so length of its height will be
`(r)/(2)`

We know that,

`\text{Volume of the cylinder}=\pi r^2h`

Putting all the values,

`\Rightarrow 1570=\pi r^2\left ((r)/(2)\right)`

`\Rightarrow (\pi r^3)/(2)=1570`

`\Rightarrow r^3=(2* 1570)/(\pi)`

`\Rightarrow r^3=999.5`

`\Rightarrow r=\sqrt[3]{999.5}`

`\Rightarrow r=9.99\approx 10`

We also know that,

`\text{Area of base}=\pi r^2=\pi * 10^2=314.16\ cm^2`