A solid metallic sphere of radius 21, cm is m | vedclass

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(A) The volume of the sphere is given by $V_s = \frac{4}{3} \pi r_1^3$,where $r_1 = 21\, cm$.The volume of the cone is given by $V_c = \frac{1}{3} \pi

Vedclass · Accepted Answer

$336$

Vedclass · Answer

(A) The volume of the sphere is given by $V_s = \frac{4}{3} \pi r_1^3$,where $r_1 = 21\, cm$.The volume of the cone is given by $V_c = \frac{1}{3} \pi r_2^2 h$,where the diameter of the base is $21\, cm$,so the radius $r_2 = \frac{21}{2}\, cm$.Since the sphere is melted and recast into a cone,their volumes are equal: $V_s = V_c$.$\frac{4}{3} \pi r_1^3 = \frac{1}{3} \pi r_2^2 h$$4 	imes (21)^3 = (\frac{21}{2})^2 	imes h$$4 	imes 21 	imes 21 	imes 21 = \frac{21}{2} 	imes \frac{21}{2} 	imes h$$4 	imes 21 = \frac{h}{4}$$h = 4 	imes 21 	imes 4 = 336\, cm$.

$A$ 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?

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