A cone of base radius 4 cm is divided into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volume of the two parts.

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Step 1: $	riangle ABC \sim 	riangle ADE$. $\frac{h}{2h} = \frac{BC}{4} \Rightarrow BC = 2$ cm
Step 2: Ratio of volumes of two parts:
$= \frac{\frac{1}{3}\pi 	imes 2^2 	imes h}{\frac{1}{3}\pi(2^2 + 4^2 + 2 	imes 4) 	imes h}$
Step 3: $= \frac{4}{28} = \frac{1}{7}$ or $1 : 7$

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