Question

Question 102

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

Answer 1

Diameter of the hollow garden roller = 42 cm

$\therefore$ Inner radius $=\frac{42}{2}=21cm$ $[\because radius=\frac{diameter}{2}]$
$\because$ Thickness of cast iron = 2 cm
$\therefore$ Outer radius = 21 + 2 = 23 cm
Volume of hollow cylinder $=\pi (R^2-r^2)\times h$ [where R is outer-radius and r is inner-radius]
$=\frac{22}{7}\times \left[\right(23{)}^2-\left(21{)}^2\right]\times 152$
$=\frac{22}{7}\times (529-441)\times 152=\frac{22}{7}\times 88\times 152=\frac{22\times 88\times 152}{7}=\frac{294272}{7}=42038.85c{m}^3$