A hemisphere is made of lead. Its radius is 6 | vedclass

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(B) Let $r \, cm$ be the radius of the base of the cone.Since the volume of the material remains constant during casting,the volume of the hemisphere

Vedclass · Accepted Answer

$2.4$

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(B) Let $r \, cm$ be the radius of the base of the cone.Since the volume of the material remains constant during casting,the volume of the hemisphere equals the volume of the cone.Volume of hemisphere = $\frac{2}{3} \pi R^3$,where $R = 6 \, cm$.Volume of cone = $\frac{1}{3} \pi r^2 h$,where $h = 75 \, cm$.Equating the volumes: $\frac{2}{3} \pi (6)^3 = \frac{1}{3} \pi r^2 (75)$.Canceling $\frac{1}{3} \pi$ from both sides: $2 	imes 216 = r^2 	imes 75$.$r^2 = \frac{432}{75} = 5.76$.Taking the square root: $r = \sqrt{5.76} = 2.4 \, cm$.

$A$ hemisphere is made of lead. Its radius is $6 \, cm$. It is cast into a right circular cone of $75 \, cm$ height. The radius of the base of the cone is ......... $cm$.

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