Question
A solid is in the shape of a cone standing on a hemisphere with both their diameters being equal to $1 \ cm$ and the height of the cone is equal to its radius. Find the volume of the solid. $[$Use $\pi=3.14 ]$
✓
Answer
Clearly $r =\frac{1}{2}, h=\frac{1}{2}$
Volume of solid $=$ Volume of Cone $+$ Volume of Hemisphere
$=\frac{1}{3} \pi r ^2 h+\frac{2}{3} \pi r ^3$
$=\frac{1}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}+\frac{2}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}$
$=\frac{1}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times\left[\frac{1}{2}+2\left(\frac{1}{2}\right)\right]$
$=\frac{1}{3} \times \frac{3.14}{4} \times \frac{3}{2}$
$=\frac{1.57}{4}$
$=\frac{157}{400} \ cm^3 \text { or } 0.3925 \ cm^3$
Volume of solid $=$ Volume of Cone $+$ Volume of Hemisphere
$=\frac{1}{3} \pi r ^2 h+\frac{2}{3} \pi r ^3$
$=\frac{1}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}+\frac{2}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}$
$=\frac{1}{3} \times 3.14 \times \frac{1}{2} \times \frac{1}{2} \times\left[\frac{1}{2}+2\left(\frac{1}{2}\right)\right]$
$=\frac{1}{3} \times \frac{3.14}{4} \times \frac{3}{2}$
$=\frac{1.57}{4}$
$=\frac{157}{400} \ cm^3 \text { or } 0.3925 \ cm^3$
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