Question

The volume V of a cylindrical can is represented by the formula V=πr2h, where h is the height and r is the radius. A cylindrical can has a volume of 1152π cubic centimeters and a height of 8 centimeters. What is the radius of the can?

Answer 1

You are given that the volume of a cylinder is
`V= \pi r^(2) h`.

You are also told that this particular cylinder (the can) has a volume of
`1152 \pi` and a height of 8. That is, for this particular cylinder the following are true:

V=
`1152 \pi`
h=8

Now we plug these values into the formula for the volume of a cylinder and solve for r. We do this as follows:


`V= \pi r^(2) h 1152 \pi = \pi r^(2)(8) 1152=8 r^(2) 144= r^(2) r=12`

Thus, the radius of the can is 12 centimeters.