Question:
A hollow cylindrical pipe is 21 dm long. Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe.
Solution:
Let the length of the cylinder pipe be $h=21, \mathrm{dm}=210 \mathrm{~cm}$.
Let the outer and the inner radius of the pipe be $R \mathrm{~cm}$ and $r \mathrm{~cm}$, re $s$ pectively.
$\therefore 2 R=10$ and $2 r=6$
$R=5 \mathrm{~cm}$ and $r=3 \mathrm{~cm}$
Volume of the copper used in making the pipe, $V=\pi\left(R^{2}-r^{2}\right) h$
$=\frac{22}{7} \times\left(5^{2}-3^{2}\right) \times 210$
$=22 \times(25-9) \times 30$
$=22 \times 16 \times 30$
$=10560 \mathrm{~cm}^{3}$