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A solid cuboidal slab of iron of dimensions $66 cm × 20 cm × 27 cm$ is used to cast an iron pipe. If the outer diameter of the pipe is $10 cm$ and thickness is $1 cm$ . Then, what is the length of the pipe?

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1200 cm

1300 cm

1260 cm

1460 cm

answer is C.

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Detailed Solution

Given that the dimensions of a solid cuboidal slab of iron are

66 cm × 20 cm × 27 cm

, its outer diameter of the pipe is 10cm and thickness is 1cm.
We have the following formulae,
Volume of cuboid =

l × b × h

Volume of cylinder

= π r 2 h

Since the outer diameter (D) is 10cm,
Inner diameter (d) = 10 - 2r
= 8cm
The inner radius will be,
r = 4cm
The outer radius will be R=5cm
The volume of the cuboid=Volume of cylinder with radius R-Volume of cylinder with radius r

66 × 20 × 27 = 227 × h 52 − 42 h = 7 × 66 × 20 × 27 22 × 9 = 1260 cm

Thus, the length of the pipe is 1260 cm.
Therefore the correct option is 3.

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