Question

A cuboid slab of iron whose dimensions are 55cm*40cm*15cm is melted and recast into a pipe. The outer radius and thickness of the pipe are 4 cm and 1 cm respectively. Find the length of the pipe.

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Answer 1

hope this explaination helps

Answer 2

Question : -

A cuboid slab of iron whose dimensions are 55cm x 40cm x 15cm is melted and recasted into a pipe. The outer radius and thickness of the pipe are 4 cm and 1cm respectively. Find the length of the pipe.

Answer : -

Given : -

Dimensions of the cuboid slab of iron

• length = 55 cm
• breadth = 40 cm
• height = 15 cm

Dimensions of the pipe

• inner radius (thickness) (r) = R - thickness = 4 - 1 = 3 cm
• outer radius (R) = 4 cm
• length of the pipe (h) = h

Required to find : -

Length of the pipe ??

Solution : -

Here,

A cuboid slab of iron is melted and re-casted into a pipe ..

The pipe is in the shape of hollow cylinder

This implies;

Volume of cuboid (slab) = Volume of hollow cylinder (pipe)

So,

Dimensions of cuboid !

• length = 55 cm
• breadth = 40 cm
• height = 15 cm

Volume of a cuboid = lbh

= 55 x 40 x 15

So, volume of cuboid = (55)(40)(15)

By the condition which we have ;

Volume of hollow cylinder = (55)(40)(15)

Dimensions of hollow cylinder !

• inner radius (thickness) (r) = 3 cm
• outer radius (R) = 4 cm
• length of the pipe (h) = h

Volume of hollow cylinder = πh(R²-r²)

So, this implies

(55)(40)(15) = (22)/(7) x (h) x [ (4)² - (3)² ]

(55) x (40) x (15) x (7)/(22) = h x [16 - 9]

(5) x (40) x (15) x (7)/(2) = h x 7

7 gets cancelled on both sides

5 x 40 x 15 x (1)/(2) = h

5 x 20 x 15 = h

75 x 20 = h

1500 = h

=> h = 1500 cm

Therefore,

• Length of the pipe (h) = 1500 cm