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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.
Solution
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
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