Question

If the area of the base of one cylinder is 452.16 square units, and the radius of another cylinder is 12 units, which additional fact must be true for the volumes of the two cylinders to be equal? (Use = 3.14)
A. The heights of each cylinder must be the same.
B. The areas of the base of each cylinder must be the same.
C. The circumferences of the base of each cylinder must be the same.
D. The radii of the base of each cylinder must be the same.

Answer 1

Answer: C. the circumferences of the base of each cylinder must be the same

Step-by-step explanation:

Answer 2

Check the picture below.

so we know that the area of the base of the 1st cylinder is 452.16, and the radius of the 2nd cylinder is 12, hmmm what is the radius of the 1st cylinder anyway?

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=452.16 \end{cases}\implies 452.16=\pi r^2\implies \cfrac{452.16}{\pi }=r^2 \\\\\\ \stackrel{\pi =3.14}{\cfrac{452.16}{3.14 }}=r^2\implies 144=r^2\implies \sqrt{144}=r\implies 12=r$

low and behold, the radius of the 1st one is 12 as well, so both cylinders have the same radius.  Let's recall the volume of a cylinder is V = πr²h.

now if they can just have the same height, they'd both have the same volume.