Question

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

Answer 1

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Answer 2

Hi there !!

Length , l = 4.4 metres

Breadth , b = 2.6 metres

Height , h = 1 metre

Volume of a cuboid = l b h

= 4.4 × 2.6 × 1

= 11.44 m³

The cuboid is melted and is made into a hollow cylindrical pipe.

But ,

Even if shape changes ,Volume of both the shapes remains same.

Volume of cuboid = Volume of hollow cylindrical pipe = 11.44 m³

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Radius ,r = 30 cm = 0.3 metres

Thickness = 5 cm = 0.05 metre

Outer radius, R = inner radius + thickness
= 0.3 + 0.05
= 0.35 metres

Height of the pipe = Length of the pipe

Volume of a cylindrical pipe = π [ R² - r ² ] × h
= 22/7 × [ (0.35)² - (0.3)² ] ×h


22/7 × [ (0.35)² - (0.3)² ] ×h = 11.44 m³

22/7 × [ 0.1225 - 0.09 ] ×h = 11.44 m³

22/7 × 0.0325 × h = 11.44 m³


h =$\frac{11.44*7}{22*0.0325}$

= $\frac{80.08}{0.715}$

= 112 metres

Length of the pipe = 112 metres