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 $$V_s$$= $$\ \frac{\ 4}{3}$$ ΟrΒ³
It is melted and recast into a right circular cone of radius r and height h.
The volume of cone $$V_c$$= $$\ \frac{\ 1}{3}$$ ΟrΒ²h
The same volume of material is used for recasting. Therefore,
$$V_s=V_c$$
$$\ \frac{\ 4}{3}$$ΟrΒ³ =Β $$\ \frac{\ 1}{3}$$Β ΟrΒ²h
h = 4r
$$\ \frac{\ h}{r}$$Β Β = 4
D is the correct answer.
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