Question

A hollow garden roller of $42cm$ diameter and length $152cm$ is made of cast iron $2cm$ thick. Find the volume of iron used in the roller.

Answer 1

Diameter of the hollow garden roller $=42cm$

$\therefore$ Inner radius $=\frac{42}{2}=21cm$ $[\because radius=\frac{diameter}{2}]$

$\because$ Thickness of cast iron $=2cm$

$\therefore$ Outer radius $=21+2=23cm$

Volume of hollow cylinder $=\pi (R^2-r^2)\times h$ [where ${}^{\prime }{R}^{\prime }$ is outer-radius and ${}^{\prime }{r}^{\prime }$ is inner-radius]

$=\frac{22}{7}\times \left[\right(23{)}^2-\left(21{)}^2\right]\times 152$

$=\frac{22}{7}\times (529-441)\times 152$

$=\frac{22}{7}\times 88\times 152$

$=\frac{22\times 88\times 152}{7}$

$=\frac{294272}{7}$
$=42038.85c{m}^3$