Question:
A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
Solution:
Given, h = 63 cm
The outer circumference of the roller = 440 cm
Thickness of the roller = 4 cm
Let, R be the external radius
We know that,
22/7 * R = 440
2 * 22/7 * R = 440
R = 70
The thickness is given as 4cm, so the inner radius 'r' is given as
⟹ r = R - 4
⟹ 70 - 4
⟹ 66cm
Here, we know the inner and outer radii
So, the volume is given as
$\Rightarrow V=\pi\left(R^{2}-r^{2}\right) h$
$=22 / 7 *\left(70^{2}-66^{2}\right) * 63$
= 22/7 * 4 * 136 * 63
$=107712 \mathrm{~cm}^{3}$
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