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 $=r=3.5cm$

height of cylinder, $h=6.5cm$
height of cone, $h^{\prime }=12.6-6.5=6.1cm$

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

$=\frac{1}{3}\pi r^2{h}^{\prime }+\pi r^{2}h+\frac{2}{3}\pi r^3$

$=\pi r^2(\frac{1}{3}{h}^{\prime }+h+\frac{2}{3}r)$

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

$=\frac{22\times 0.5\times 3.5}{1}(2.033+6.5+2.333)$

$=38.5(2.033+6.5+2.333)$

$=38.5\times 10.866$

$=418.35c{m}^3$