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 =
`(r)/(2)`

Given : The Volume of the Pool = 1570 feet³

⇒ πr²h = 1570

⇒
`\pi (r^2)((r)/(2)) = 1570`

⇒
`((22)/(7))((r^3)/(2)) = 1570`

⇒
`(22r^3)/(14) = 1570`

⇒
`r^3 = (1570* 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