Question

A solid cuboid of iron with dimensions 53 cm ⨯ 40 cm ⨯ 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe. [CBSE 2015]

Answer 1

Volume of solid cuboid of iron = Volume of cylindrical pipe
$$\begin{gathered} \Rightarrow lbh=\mathrm{\pi }h\left(R^2-r^2\right) \\ \Rightarrow 53\times 40\times 15=\frac{22}{7}\times h\left[{\left(\frac{8}{2}\right)}^2-{\left(\frac{7}{2}\right)}^2\right] \\ \Rightarrow 53\times 40\times 15=\frac{22}{7}\times h\left[4^2-{\left(3.5\right)}^2\right] \\ \Rightarrow 53\times 40\times 15=\frac{22}{7}\times h\times 3.75 \\ \Rightarrow h=2698.18\mathrm{cm} \end{gathered}$$


Disclaimer: The answer given in the book is not correct.