Question

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?

Answer 1

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

==================================

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
=  $\frac{22}{7}$× [ (0.35)² - (0.3)² ] ×h


   $\frac{22}{7}$ × [ (0.35)² - (0.3)² ] ×h = 11.44 m³

   $\frac{22}{7}$ × [ 0.1225 - 0.09 ] ×h = 11.44 m³

   $\frac{22}{7}$ × 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

Answer 2

Sorry for all those dirty cuts and crosses