A hollow sphere of internal and external diam | vedclass

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(B) The volume of a hollow sphere is given by $V = \frac{4}{3} \pi (R^3 - r^3)$,where $R$ is the external radius and $r$ is the internal radius.Given:

Vedclass · Accepted Answer

$14$

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(B) The volume of a hollow sphere is given by $V = \frac{4}{3} \pi (R^3 - r^3)$,where $R$ is the external radius and $r$ is the internal radius.Given: External diameter $= 8\,cm \implies R = 4\,cm$. Internal diameter $= 4\,cm \implies r = 2\,cm$.Volume of the hollow sphere $= \frac{4}{3} \pi (4^3 - 2^3) = \frac{4}{3} \pi (64 - 8) = \frac{4}{3} \pi 	imes 56\,cm^3$.When the sphere is melted into a cone,the volume remains constant.Volume of cone $= \frac{1}{3} \pi r_{cone}^2 h$.Given: Base diameter of cone $= 8\,cm \implies r_{cone} = 4\,cm$.Equating the volumes: $\frac{1}{3} \pi (4)^2 h = \frac{4}{3} \pi 	imes 56$.$16h = 4 	imes 56$.$h = \frac{224}{16} = 14\,cm$.

$A$ hollow sphere of internal and external diameters $4\,cm$ and $8\,cm$ respectively is melted into a cone of base diameter $8\,cm$. The height of the cone is......$cm$.

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