Question

if the radius of a cylinder is doubled, the volume will increase by a factor of ____. a. 2 b. 3 c. 8 d. 4

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 $r_1$

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

Step3: New radius is $r_2 = 2r_1$

The new - volume $V_2=\pi(2r_1)^{2}h=\pi\times4r_1^{2}h = 4(\pi r_1^{2}h)$.

Step4: Find the factor of increase

Since $V_2 = 4V_1$, the volume increases by a factor of 4.

Answer:

D. 4