Question

A hollow garden roller, $63cm$ wide with a girth of $440cm$, is made of $4cm$ thick iron. Find the volume of the iron.

Answer 1

Width of hollow cylinder (h) $=63cm$

Girth (Perimeter) $=440cm$

$\therefore Radius=\frac{\text{Perimeter}}{2\pi }=\frac{440\times 7}{2\times 22}=70cm$

Thickness of iron $=4cm$

$\therefore$ Inner radius $=70-4=66cm$

$\therefore$ Volume of iron used $=\pi h(R^2-r^2)$

$=\frac{22}{7}\times 63\times ({70}^2-{66}^2)c{m}^3$

$=198(70+66)(70-66)$ $c{m}^3$ [Since, $a^2-b^2)=(a-b\left)\right(a+b)$]

= $198\times 136\times 4c{m}^3=107712c{m}^3$