If the radius of the base and height of a cylinder and cone are each equal to r, and the radius of a hemisphere is also equal to r, then the volumes of the cone, cylinder and hemisphere are in the ratio ?
Options:
A . 1 : 2 : 3
B . 1 : 3 : 2
C . 2 : 1 : 3
D . 3 : 2 : 1
Answer: Option B Required ratio : = Volume of cone : Volume of cylinder : Volume of hemisphere $$\eqalign{ & = \frac{1}{3}\pi {r^2}:\pi {r^2}r:\frac{2}{3}\pi {r^3} \cr & = \frac{1}{3}:1:\frac{2}{3} \cr & = 1:3:2 \cr} $$
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