Question

A metal place has a bore (inner diameter) of 5 cm.The pipe is 5 mm thick all around.Find the weight,in kilogram,of 2 meters of the pipe if $1c{m}^3$ of the metal weighs 7.7 g.

Answer 1

The inner diameter = 5cm
The inner radius = $\frac{5}{2}$ = 2.5 cm
The thickness = 5 mm = $\frac{5}{10}$cm = 0.5cm

The outer radius = 2.5 + 0.5 = 3 cm

The length of the pipe = 2 m = 2 x 100 cm = 200 cm

Volume of the pipe = $\frac{22}{7}\times R^2\times h$ - $\frac{22}{7}\times r^2\times h$ = $\frac{22}{7}\times (R^2-r^2)\times h$
Where R = outer radius, r = inner radius and h = length of pipe


∴ Volume = $\frac{22}{7}\times (3^2-{2.5}^2)\times 200$
= $\frac{22}{7}\times (9-6.25)\times 200$
= 1728.57 $c{m}^3$
Mass = Density x Voulme
= 7.7 x 1728.57
= 13310 g

1000g = 1kg
∴ Mass = $\frac{13310}{1000}$ = 13.31 kg