Question 126

A solid metallic sphere of radius 21 cm is melted and recast into a cone with diameter of the base as 21 cm. What is the height (in cm) of the cone?

Solution

Radius of sphere, $$R=21$$ cm

Let height of cone = $$h$$ cm and radius of cone = $$r=\frac{21}{2}$$ cm

According to ques, Volume of cone = Volume of sphere

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

=> $$(\frac{21}{2})^2\times h=4\times (21)^3$$

=> $$h=4\times4\times\frac{(21)^3}{(21)^2}$$

=> $$h=16\times21=336$$ cm

=> Ans - (A)

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