The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe

Mensuration (C10)

The dimensions of a solid iron cuboid are 4.4 m × 2.6 m × 1.0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe.

Solution

Volume of cuboid = 4.4 × 2.6 × 1 m3

Inner and outer radii of cylindrical pipe = 30 cm, 35 cm

Volume of material used = π/1002 (352 - 302) × h m3

= π/1002 × 65 × 5h m3

Now, volume of material used = volume of cuboid

π/1002 × 65 × 5h = 4.4 × 2.6

h = 112 m