Answer: C

The volume of cylinder A is $\pi r^2 h$. The volume of cylinder B is $\pi(2r)^2\left(\frac{h}{2}\right) = \pi(4r^2)\left(\frac{h}{2}\right) = 2\pi r^2 h$. So the volume of cylinder B is $2$ times the volume of cylinder A.

Choice B assumes that doubling the radius and halving the height cancel out, but the radius is squared in the volume formula, so doubling it multiplies the volume by $4$.

Why the other choices are wrong

• A. This considers only the halved height and ignores the doubled radius.
• B. The radius is squared, so doubling it multiplies the volume by 4, while halving the height divides by only 2.
• D. 4 accounts for the doubled radius but forgets that the height was cut in half.