Question

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 $10cm$ and its base is of radius $3.5cm$, find the volume of wood in the toy.

Answer 1

We have,

Radius of the cylinder = Radius of the hemisphere $=r=3.5cm$ and

Height of the cylinder, $h=10cm$

Now,

Volume of the toy = Volume of the cylinder - Volume of the two hemispheres

= $\pi r^{2}h$ $-2\times \frac{2}{3}$$\pi r^3$

= $\pi r^2(h-\frac{4r}{3}$)
= $\pi r^2(10-\frac{4\times 3.5}{3}$)

= $\pi r^2(10-\frac{14}{3}$)

= $\pi r^2(\frac{16}{3}$)

= $\frac{22}{7}\times 3.5\times 3.5\times (\frac{16}{3}$)

=$\frac{616}{3}$ $c{m}^3$

= $205.33c{m}^3$

So, the volume of wood in the toy is $\frac{616}{3}$ $c{m}^3$ or 205.33 $c{m}^3$.