Question 61

The volume of a right circular cone is equal to that of a sphere, whose radius is half the radius of the base of the cone. What is the ratio of the radius ofthe base to the height of the cone ?

Solution

Volume of right circular cone = Volume of sphere

$$\frac{1}{3}\pi\ r^2h=\frac{4}{3}\pi\ r^3$$

$$r^2h=4\left(\frac{r}{2}\right)^3$$ (radius of sphere = half of radius of base of cone)

$$h=\frac{r}{2}$$

r : h = 2 : 1.

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