Question

A metal pipe has a bore (inner diameter) of 5 cm. The pipe is 5 mm thick all round. Find the weight, in kilogram, of 2 metres of the pipe if 1 cm³ of the metal weights 7.7 g.

Answer 1

Inner radius of the pipe = r

= `5/2` cm

= 2.5 cm

External radius of the pipe = R

= Inner radius of the pipe + Thickness of the pipes

= 2.5 cm + 0.5 cm

= 3 cm

Length of the pipe = h

= 2 m

= 200 cm

Volume of the pipe = External volume – Internal volume

= `piR^2h - pir^2h`

= `pi(R^2 - r^2)h`

= `22/7(3^2 - (5/2)^2) xx 200`

=  `22/7 xx (9 - 25/4) xx 200`

= `22/7 xx ((36 - 25)/4) xx 200`

= `22/7 xx 11/4 xx 200`

= `(22/7 xx 550)`

= 1728.6 cm³ 

Since 1 cm³ of the metal weights 7.7 g,

∴ Weight of the pipe = (1728.6 × 7.7)g

= `(1728 xx 7.7/1000) kg`

= 13.31 kg