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

`\sqrt[3]{3140^2\pi}\approx 146.41\ ft^2`

Explanation:

The volume of the cylinder is

`V_(cylinder)=\pi r^2\cdot H,`

where r is the base radius and H is the height.

Since
`H=(1)/(2)r` and V=1570 cubic feet, then

`1570=\pi r^2\cdot (r)/(2),\\ \\1570=(\pi r^3)/(2),\\ \\r^3=(3140)/(\pi),\\ \\r=\sqrt[3]{(3140)/(\pi)}\ ft.`

The area of its bottom floor is

`A_(floor)=\pi r^2=\pi\cdot \left(\sqrt[3]{(3140)/(\pi)}\right)^2= \sqrt[3]{3140^2\pi}\approx 146.41\ ft^2.`