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.

Answer 1

Given,

The outer and inner diameters of pipe are 8 cm and 7 cm.

Dimensions of a solid cuboid of iron = 53 cm × 40 cm × 15 cm.

When a shape melted and recast into another shape volume will remain same.

Volume of cubical iron = volume of cylindrical pipe

length × breadth × height = π(R² − r²)h

53 × 40 × 15 = `22/7 xx (4^2 - (7/2)^2)h`

53 × 40 × 15 = `22/7 xx 15/4 xx h`

h = `(53 xx 40 xx 15 xx 7 xx 4)/(22 xx 15)`

h = 2698.18 cm = 27 m [∵ 1 m = 100 cm]