The volume of a right circular cylinder is 72\pi. If the radius of the base of the cylinde… — SAT

The volume of a right circular cylinder is $72\pi$ . If the radius of the base of the cylinder is $3$ , what is the height of the cylinder?

Answer: 8

The height of the cylinder is 8.

The volume

V

of a right circular cylinder is given by the formula

V = \pi r^2 h

, where

r

is the base radius and

h

is the height. By substituting the given volume of

72\pi

and radius of

3

, we obtain the equation

72\pi = \pi (3)^2 h

. Simplifying the right side gives

72\pi = 9\pi h

. Dividing both sides of the equation by

9\pi

isolates the height, giving

h = 8

Use the formula for the volume of a right circular cylinder.

V = \pi r^2 h

This formula relates the volume, radius, and height of a cylinder.

Substitute the known values into the volume formula.

72\pi = \pi (3)^2 h

To form an equation with the unknown height.

Simplify the squared radius and isolate the variable.

h = 8

Simplifying

3^2

gives

9

. Dividing

72\pi

9\pi

isolates the height.

Solving for an unknown dimension using the volume formula of a cylinder.

Estimated Time:45s

Question