Discussion
Using the clay, Malar makes a cone, a hemisphere and a cylinder have equal bases and the heights of the cone and a cylinder are equal. They same as the common radius then find the ratio of their respective volumes
Answer: A
The ratio of the volumes is 1 : 2 : 3.
With a common radius \(r\) and the heights of the cone and cylinder equal to \(r\) (the hemisphere's height is \(r\) anyway):
\[ \begin{aligned} \text{cone} &= \tfrac{1}{3}\pi r^{3} \\ \text{hemisphere} &= \tfrac{2}{3}\pi r^{3} \\ \text{cylinder} &= \pi r^{3} \end{aligned} \]
Multiplying by 3 gives 1 : 2 : 3, Archimedes' classic result. The ratios 1 : 2 : 4, 1 : 2 : 5 and 1 : 2 : 6 overstate the cylinder, whose volume is exactly three times the cone's.
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