A wooden toy was made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy.[ use $\pi =\frac{22}{7}$].
Given: Height of the solid cylinder $=10\ cm$. and radius its base $=3.5\ cm$
What to do: To find the volume of wood in the toy made by scooping out a hemisphere of same radius from each end of the given cylinder.
Solution:
Height of the cylinder, $h=10\ cm$
Radius of the cylinder = Radius of each hemisphere, $r=3.5\ cm$
Volume of each hemisphere$=\frac{2}{3} \pi r^{3}$
Volume of the cylinder $=\pi r^{2} h$
$\therefore$ Volume of wood in the toy$=$Volume of cylinder $-2\times$ Volume of each hemisphere
$=\pi r^{2} h-2\times \frac{2}{3} \pi r^{3}$
$=\pi r^{2}\left( h-2\times \frac{2}{3} r\right)$
$=\frac{22}{7} \times 3.5\times 3.5( 10-2\times \frac{2}{3} \times 3.5)$
$=38.5\times 5.33$
$=205.205\ cm^{3} $
Therefore the volume of wood in the toy is $205.205\ cm^{3}$.
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