Question

One cup is equal to 14.4375 in^3. If a 1-cup measuring cylinder has a radius of 3 in., what is its height? If

the radius is 1 in., what is its height? Round to the nearest tenth.

If the measuring cup has a radius of 3 in. then its height is

height is _____ in., and it it has a radius of 1 in. then it’s height is _____ in.

Answer 1

The height of the cup is 0.51 in.

The height of the cup is 4.59 in.

Explanation:

The volume of the cylinder is
`\pi r^2 h`

Given that,

The volume of the cup is 14.4375 in³.

If the measuring cup has a radius of 3 in.

Then,

`\pi r^2h=14.4375`

Plug r= 3 in.

`\pi (3)^2h=14.4375`

`\Rightarrow h=(14.475)/(9\pi )`

⇒h=0.51 in.

The height of the cup is 0.51 in.

If it has radius of 1 in.

Then,

`\pi r^2h=14.4375`

Plug r= 1 in.

`\pi (1)^2h=14.4375`

`\Rightarrow h=(14.475)/(1\pi )`

⇒h=4.59 in.

The height of the cup is 4.59 in.