Question

Determine whether the statement is true or false.

A sphere with volume 972pi cubic inches has surface area 324pi square inches.

Answer 1

True

Explanation:

Given

Shape: Sphere

`Volume = 972\ pi`

`Area = 324\pi`

Required

True or False

The volume of a sphere is:

`Volume = (4)/(3)\pi r^3`

Substitute
`972\pi` for volume

`972\pi = (4)/(3)\pi r^3`

`972 = (4)/(3)r^3`

Make r the subject

`r^3 = (3)/(4) * 972`

`r^3 = (3 * 972)/(4)`

`r^3 = (2916)/(4)`

`r^3 = 729`

`r =9`

The surface area is calculated using:

`Area =4\pi r^2`

`Area =4\pi *9^2`

`Area =4\pi *81`

`Area =324\pi`