Question

a certain cylinder has a radius of r inches. its volume in cubic inches is given by the expression 2πr³. which statement about the cylinder must be true? a. the cylinder’s radius is 2 inches. b. the cylinder’s height is 2 inches. c. the cylinder’s radius is 2 times its height. d. the cylinder’s height is 2 times its radius. (1 point) o a o b o c o d

Explanation:

Step1: Recall volume formula for cylinder

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

Step2: Equate given and standard volume formulas

We are given $V = 2\pi r^{3}$, and $V=\pi r^{2}h$. So, $\pi r^{2}h=2\pi r^{3}$.

Step3: Solve for $h$

Divide both sides of the equation $\pi r^{2}h = 2\pi r^{3}$ by $\pi r^{2}$ (assuming $r
eq0$). We get $h = 2r$.

Answer:

D. The cylinder’s height is 2 times its radius.