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 $2$ meters of the pipe, if $1$ $c{m}^3$ of the metal weights $7.7$ g.

• A. $14.31$ kg
• B. $10.31$ kg
• C. $13.31$ kg
• D. $11.31$ kg

Answer 1

Answer: (C)

$13.31$ kg

Given, Inner diameter $=5$ cm. radius $=2.5$ cm
Thickness $=5$ mm $=0.5$ cm
Outer radius $=2.5+0.5=3$ cm
Length $=2$ m$=200$ cm
Volume of pipe $=V=\pi {(R}^2-r^2)h$
$\Rightarrow V=\frac{22}{7}{(3}^2-{2.5}^2)\times 200$
$\Rightarrow V=\frac{22}{7}(9-6.25)\times 200$
$\Rightarrow V=\frac{12100}{7}{cm}^3$
Therefore, $1c{m}^3$ of the metal weighs $7.7$ g.
So, $\frac{12100}{7}{cm}^3$ weighs $=7.7\times \frac{12100}{7}$ g$=13310$ g
$\therefore 13310$ g$=\frac{13310}{1000}$ kg$=13.31$ kg