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.