# If a right circular cylinder has a volume of 144pi and a height of 9, what is the area of its base? is it: a. 8 pi b. 12 pi c. 16 pi d. 25 pi or e. 32 piPlease explain the process.

samhouston | Certified Educator

The formula for volume of a cylinder is...

V = r^2 * h * pi

Given that the volume is 144pi and the height is 9, you can write the following equation using substitution

144(pi) = 9r^2(pi)

Divide both sides by pi.

144 = 9r^2

Divide by sides by 9.

16 = r^2

Square root both sides.

4 = r

Since the area of the base of a cylinder is a circle, the formula is...

A = pi * r^2

Substitute 4 in for the variable r.

A = pi * 16

giorgiana1976 | Student

We'll recall the formula that gives the volume of a right circular cylinder:

V = Abase*height

Since the base of cylinder is a circle, the area of the circle is:

A = pi*r^2

We'll substitute all the given data within the formula of volume:

144pi = pi*r^2*9

Abase = 144pi/9

Abase = 16 pi

The area of the base of the right cylinder is Abase = 16 pi, therefore the right option is c. 16 pi.