Question

a film canister in the shape of a cylinder has a height of 8 centimeters and a volume of the film canister. write an equation for the volume of the film canister.

Answer 1

Part a) The equation for the volume of the film canister is

`32\pi=\pi r^(2)(8)`

Part b) The radius of the film canister is
`2\ cm`

Explanation:

The complete question is

A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.

a. Write an equation for the volume of the film canister.

b. What is the radius of the film canister?

Part a) Write an equation for the volume of the film canister

we know that

The volume of a cylinder is equal to

`V=\pi r^(2) h`

where

r is the radius of the circular base

h is the height of the cylinder

we have

`V=32\pi\ cm^3`

`h=8\ cm`

substitute

`32\pi=\pi r^(2)(8)` ----> equation for the volume of the film canister

Part b) What is the radius of the film canister?

we have

`32\pi=\pi r^(2)(8)`

`32\pi=8\pi r^(2)`

Simplify

Divide by 8π both sides

`4=r^(2)`

square root both sides

`r=2\ cm`