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

Answer:

The area of its bottom floor is 314.16 cm²

Step-by-step 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 $\dfrac{r}{2}$

We know that,

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

Putting all the values,

$\Rightarrow 1570=\pi r^2\left (\dfrac{r}{2}\right)$

$\Rightarrow \dfrac{\pi r^3}{2}=1570$

$\Rightarrow r^3=\dfrac{2\times 1570}{\pi}$

$\Rightarrow r^3=999.5$

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

$\Rightarrow r=9.99\approx 10$

We also know that,

$\text{Area of base}=\pi r^2=\pi \times 10^2=314.16\ cm^2$