Question

The dimensions of a solid iron cuboid are 4.4 m x 2.6 m x 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

Hi friend ,

The volume of the solid iron cuboid = l×b×h

length of the cuboid = 4.4 m = 440 cm

breadth of the cuboid = 2.6 m = 260cm

Height of the cuboid = 1.0 m = 100 cm

Volume = 440×260×100
= 11440000 cm ^3

Volume of the cuboid = Vol. of the cylindrical pipe
Vol. of the cylindrical pipe = 11440000cm ^3

Inner radius of the pipe = 30 cm

Outer radius of the pipe = 35 cm

π (R^2 - r^2 ) h = 11440000

22/7 [ (35×35) - (30×30) × h = 11440000

22/7 [ 1224 - 900] × h = 11440000

22/7 [324] × h = 11440000

1018.28× h = 11440000
h = 11440000/1018.28

h = 11234.63cm
h = 112.34m
---------------------------------
Hope this helped u..
PLZ MARK AS BRAINLIEST...