Question 74

The volume of a right circular cone, with a base radius the same as its altitude, and the volume of a hemisphere are equal. The ratio of the radii of the cone to the hemisphere is:

Solution

Volume of cone = $$\frac{1}{3}\pi\ r^2h=\frac{1}{3}\pi\ r^3$$ (radius and height are equal)

Volume of hemisphere = $$\frac{2}{3}\pi\ R^3$$

Volumes of both are equal,

$$\frac{1}{3}\pi\ r^3=\frac{2}{3}\pi\ R^3$$

$$\frac{r^3}{R^3}=\frac{2}{1}$$

Required ratio = $$\sqrt[\ 3]{2}:\ 1$$

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