Question 127

A solid metallic sphere of radius 14 cm is melted and recast into a cone with diameter of the base as 14 cm. What is the height (in cm) of the cone?

Solution

Radius of sphere, $$R=14$$ cm

Let height of cone = $$h$$ cm and radius of cone = $$r=\frac{14}{2}=7$$ cm

According to ques, Volume of cone = Volume of sphere

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

=> $$(7)^2\times h=4\times (14)^3$$

=> $$h=4\times14\times\frac{196}{49}$$

=> $$h=56\times4=224$$ cm

=> Ans - (D)

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