Discussion
A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is
Answer: B
With the same base radius and the same height:
\[ V_{\text{cylinder}} = \pi r^{2} h, \qquad V_{\text{cone}} = \frac{1}{3}\pi r^{2} h \]
\[ \frac{V_{\text{cylinder}}}{V_{\text{cone}}} = \frac{\pi r^{2} h}{\tfrac{1}{3}\pi r^{2} h} = 3 \quad\Longrightarrow\quad 3 : 1 \]
Three coneloads of water exactly fill the matching cylinder - the standard classroom demonstration of where the \( \tfrac{1}{3} \) comes from.
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