Question

The Sunny Days Apartment building has a cylindrical, above ground pool in the yard. The radius of the pool is 1.5 times its height, and the volume is 1200 cubic feet. How deep is the pool? In other words, what is the height of the pool

Answer 1

5.54 feet.

Explanation:

Let h be the height of the pool and r be the radius of the pool.

We have been given that volume of cylindrical pool in Sunny Days Apartment building is 1200 cubic feet.

We have been given that the radius of the pool is 1.5 times its height. We can represent this information in an equation as:

`r=1.5*h...(1)`

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

Substituting equation (1) in volume formula we will get,

`\text{Volume of cylindrical pool}=\pi (1.5h)^2*h`

Substituting the given volume of pool in formula we will get,

`1200=\pi (1.5h)^2*h`

`1200=\pi*2.25*h^2*h`

`1200=\pi*2.25*h^3`

Let us divide both sides of our equation by 2.25 pi.

`(1200)/(2.25\pi)=(\pi*2.25*h^3)/(2.25\pi)`

`169.7652726=h^3`

Let us take cube root of both sides of our equation.

`\sqrt[3]{169.7652726}=h`

`5.537=h`

`h=5.537\approx 5.54`

Therefore, the height of the pool is approximately 5.54 feet.