A solid metallic spherical ball of diameter 6 | vedclass

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Question

(B) The volume of the spherical ball is given by the formula $V = \frac{4}{3} \pi r^3$. Given the diameter is $6\, cm$,the radius $r = 3\, cm$.Volume

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) The volume of the spherical ball is given by the formula $V = \frac{4}{3} \pi r^3$. Given the diameter is $6\, cm$,the radius $r = 3\, cm$.Volume of spherical ball $= \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36 \pi\, cm^3$ $...(1)$The volume of a cone is given by $V = \frac{1}{3} \pi R^2 h$. Given the diameter of the base is $12\, cm$,the radius $R = 6\, cm$.Volume of cone $= \frac{1}{3} \pi (6)^2 h = \frac{1}{3} \pi (36) h = 12 \pi h$ $...(2)$Since the sphere is melted and recast into the cone,their volumes must be equal.Equating $(1)$ and $(2)$,we get:$12 \pi h = 36 \pi$$h = \frac{36 \pi}{12 \pi} = 3\, cm$Therefore,the height of the cone is $3\, cm$.

$A$ solid metallic spherical ball of diameter $6\, cm$ is melted and recast into a cone with diameter of the base as $12\, cm$. The height of the cone is........$cm$

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