Question

A hollow cylindrical copper pipe is 21 dm long. If its outer and inner diameters are of 10 cm and 6 cm respectively, find the volume of the copper used in making the pipe. [Take $\pi =\frac{22}{7}$] [3 MARKS]

Answer 1

Let R and r respectively be the external and internal radii of the given hollow cylindrical copper pipe.

Then, we have
$R=\frac{1}{2}\times 10cm=5cm$ and $r=\frac{1}{2}\times 6cm=3cm$
The length (i.e. height) of the pipe (h) = 21 dm
= 210 cm
$\therefore$ Volume of the copper used in making the pipe
$=\pi h(R^2-r^2)$
$=\frac{22}{\text{/}7}\times \text{/}{210}^{30}\times (5^2-3^2)c{m}^3$
$=660(25-9)c{m}^3=660\times 16c{m}^3$
$=10560c{m}^3$
Hence, the volume of the copper used in making the pipe is $10560c{m}^3$