Question

if the radius of a cylinder is doubled, how does the volume change?
a. it doubles.
b. it quadruples.
c. it halves.
d. it stays the same.

Explanation:

Step1: Recall volume formula

The volume formula of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Let original radius be $r_1$

Original volume $V_1=\pi r_1^{2}h$.

Step3: New radius is $r_2 = 2r_1$

New volume $V_2=\pi(2r_1)^{2}h=\pi\times4r_1^{2}h = 4V_1$. So the volume quadruples.

Answer:

B. It quadruples.