Discussion
The radius of the base and height of a cone are 3 cm and 5 cm respectively whereas the radius of the base and height of a cylinder are 2 cm and 4 cm respectively. The ratio of the volume of cone to that of the cylinder is:
Answer: C
The ratio of the volumes is 15:16.
A cone holds one third of the cylinder on the same base and height: \(V = \tfrac{1}{3}\pi r^2 h\) for the cone and \(V = \pi r^2 h\) for the cylinder.
\[ \begin{aligned} \text{cone} &= \tfrac{1}{3}\pi \times 3^2 \times 5 = 15\pi \\ \text{cylinder} &= \pi \times 2^2 \times 4 = 16\pi \end{aligned} \]
So the ratio is \(15\pi : 16\pi = 15 : 16\).
45:16 is the answer if the one third in the cone formula is forgotten. 15:8 halves the cylinder by mistake, and 1:3 is the cone-to-cylinder ratio only when both share the same base and height, which these do not.
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