Question

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter Is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Answer 1

Inner diameter of tube =12 cm.

$\therefore$ Inner radius $\left(r\right)=\frac{12}{2}=6cm.$

Thickness of metal =1 m.

$\therefore$ Outer radius (R)=6+1=7 cm.

Length of the tube (h)=1 m =100 cm.

$\therefore$ Volume of metal used $=\pi R^{2}h-\pi r^{2}h$

$=\pi h(R^2-r^2)=\pi h(R+r)(R-r)$

$=\frac{22}{7}\times 100(7+6)(7-6)c{m}^3$

$=\frac{2200}{7}\times 13\times 1c{m}^3=\frac{28600}{7}c{m}^3$

Weight of $1c{m}^3$ metal =7.7 g.

$\therefore$ Total weight $=\frac{28600}{7}\times 7.7g=31460g$
=31.46 kg.