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

We know that Volume of Cylinder is given by : πr²h

Where : 'r' is the Radius of the Cylinder

             'h' is the Height or Depth of the Cylinder

Given : The Height of the Pool is Half of its Radius

⇒ Height of the Pool =  $\frac{r}{2}$

Given : The Volume of the Pool = 1570 feet³

⇒ πr²h = 1570

⇒ $\pi (r^2)(\frac{r}{2}) = 1570$

⇒ $(\frac{22}{7})(\frac{r^3}{2}) = 1570$

⇒ $\frac{22r^3}{14} = 1570$

⇒ $r^3 = \frac{1570\times 14}{22} = 999$

⇒ $r = \sqrt[3]{999} = 10\;(approx)$

As : Area of the Bottom of the Pool is Circular

We know that Area of Circle is given by : πr²

⇒ Area of the Bottom Floor = π × 10² = 314.15 feet²