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.
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
Your answer is 16pi (option c)
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.