Question 105

A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height and radius of the cone so formed?

Solution

Let the radius of solid sphere be r.

The volume of sphere $$V_s$$= $$\ \frac{\ 4}{3}$$ πr³

It is melted and recast into a right circular cone of radius r and height h.

The volume of cone $$V_c$$= $$\ \frac{\ 1}{3}$$ πr²h

The same volume of material is used for recasting. Therefore,

$$V_s=V_c$$

$$\ \frac{\ 4}{3}$$πr³ = $$\ \frac{\ 1}{3}$$ πr²h

h = 4r

$$\ \frac{\ h}{r}$$ = 4
D is the correct answer.

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