Question

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

Answer 1

solution :-

here, given that

Length , l = 4.4 metres

Breadth , b = 2.6 metres

Height , h = 1 metre
so,
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


now, 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

therefore , Height of the pipe = Length of the pipe

so , 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 = 11.44×7/22×0.0325

= 80.08/ 0.715

= 112 metres..

therefore, Length of the pipe = 112 metres(Ans)..

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

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

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