Question
A solid is in the shape of a cone surmounted on a hemisphere with both their diameters being equal to $7 \ cm$ and the height of the cone is equal to its radius. Find the volume of the solid.
✓
Answer
Radius of hemisphere $=$ radius of cone $=\frac{7}{2} \ cm$
Height of cone $=\frac{7}{2} \ cm$
Volume of the solid $=$ Volume of hemisphere $+$ Volume of cone
$=\frac{2}{3} \pi r ^3+\frac{1}{3} \pi r ^2 h$
$=\frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}\left(2 \times \frac{7}{2}+\frac{7}{2}\right)$
$=\frac{539}{4} \ cm^3$ or $134.75 \ cm^3$
Height of cone $=\frac{7}{2} \ cm$
Volume of the solid $=$ Volume of hemisphere $+$ Volume of cone
$=\frac{2}{3} \pi r ^3+\frac{1}{3} \pi r ^2 h$
$=\frac{1}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}\left(2 \times \frac{7}{2}+\frac{7}{2}\right)$
$=\frac{539}{4} \ cm^3$ or $134.75 \ cm^3$
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