Question

The given figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

Answer 1

Radius of cone = radius of cylinder = radius of hemisphere = 3.5cm
height of cylinder = 6.5cm
height of cone = 12.6 - 6.5 = 6.1 cm

Volume of Solid = Volume of cone + Volume of cylinder + Volume of hemisphere

=$\frac{1}{3}\pi r^2{h}_{cone}+\pi r^2{h}_{cyl}+\frac{2}{3}\pi r^3$

=$\pi r^2(\frac{1}{3}{h}_{cone}+h_{cyl}+\frac{2}{3}r)$

=$\frac{22}{7}\times 3.5\times 3.5(\frac{1}{3}\times 6.1+6.5+\frac{2}{3}\times 3.5)$

=$\frac{385}{10}(2.033+\frac{65}{10}+\frac{23.33}{10})$

=$\frac{385}{10}\times 10.866$

=418.341 $c{m}^3$