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:
Here, R = Outer radius
r = Inner radius
t = Thickness = 4 cm
w = Width = 63 cm
Girth = 440 cm = 2πR
$\mathrm{R}=\frac{440}{2 \times \frac{22}{7}}=70 \mathrm{~cm}$
r = R − t = 70 cm − 4 cm = 66 cm
Volume of the iron $=\pi\left(R^{2}-r^{2}\right) w=\frac{22}{7}-\left(70^{2}-66^{2}\right)-(63)=107712 \mathrm{~cm}^{3}$
Hence, volume of the iron is 107712 cm3.