Question

If 1 cm³ of case iron weighs 21 g, find the weight of a cast iron pipe of length 1 m with a bore of 3 cm in which the thickness of the metal is 1 cm.

Answer 1

Internal radius of the pipe = 1.5 cm
External radius of the pipe = (1.5 + 1) cm = 2.5 cm
Height of the pipe = 1 m = 100 cm
Volume of the cast iron = total volume of the pipe − internal volume of the pipe
$$\begin{gathered} =\mathrm{\pi }\times (2.5{)}^2\times 100-\mathrm{\pi }\times {\left(1.5\right)}^2\times 100 \\ =\frac{22}{7}\times 100\times \left[6.25-2.25\right] \\ =\frac{2200}{7}\times 4=\frac{8800}{7}{\mathrm{cm}}^3 \end{gathered}$$
1 cm³ of cast iron weighs 21 g.

∴ Weight of $\frac{8800}{7}{\mathrm{cm}}^3$cast iron = $\frac{8800}{7}\times \frac{21}{1000}\mathrm{kg}=88\times 0.3=26.4\mathrm{kg}$