Question

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chapter surface area and volume class 10th CBSE:-

the dimension of a solid iron cuboid are 4.4 m X 2.6 m. X 1.0 metre it is melted and recast into a hollow cylindrical pipe of 30cm in a radius and thickness 5 cm find the length of the pipe....?


thx for help
.fri

Answer 1

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
=  π × [ (0.35)² - (0.3)² ] ×h

π × [ (0.35)² - (0.3)² ] ×h = 11.44 m³

    π × [ 0.1225 - 0.09 ] ×h = 11.44 m³

  π × 0.0325 × h = 11.44 m³

h =(11.44 × 7)/ 22× 0.0325

 = 112 metres

Length of the pipe = 112 metres


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Answer 2

See
Volume of cuboid will be equal to volume of cylindrical
It means
Calculation 1m = 100 cm
Volume of solid cuboid =440×260×100=11440000cm^3
Thickness is 5 cm
Internal radius =r=30 cm
External radius=R=30+5=35 cm
Volume of hollow cylindrical=πh(R^2-r^2)
πh(325)
Volume of cuboid will be equal to volume of cylindrical
325πh=11440000
h=11440000×1/π×1/325
h=1600×7
=11200
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