Question:
Find the mass of a 3.5 m long lead pipe, if the external diameter of the pipe is 2.4 cm, thickness of the metal is 2 mm and the mass of 1 cm3 of lead is 11.4 grams.
Solution:
Length of the pipe (h) = 3.5 cm = 300 cm
External radius of the pipe $(R)=\frac{2.4}{2}=1.2 \mathrm{~cm}$
Thickness of pipe $=2 \mathrm{~mm}$
$=0.2 \mathrm{~cm}$
So internal radius of pipe $=1.2-0.2$
$=1 \mathrm{~cm}$
Thus volume of pipe $=\pi\left(R^{2}-r^{2}\right) h$
$=\frac{22}{7} \times\left((1.2)^{2}-1^{2}\right) \times 300$
$=22 \times 50 \times 0.44 \mathrm{~cm}^{3}$
$=484 \mathrm{~cm}^{3}$
Mass of 1 cm3 pipe is 11.4 gm
Total mass = 4184 × 11.4 = 5517.6 gm = 5.518 kg.