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# A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

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We have to find the length of the pipe given that,
A solid cuboid of iron with dimensions 53 cm x 40 cm x 15 cm is
melted and recast into a cylindrical pipe. The outer and inner
diameters of pipe are 8 cm and 7 cm respectively.

One of the important question for the board exam class 10 from
mensuration chapter.This question is from r d sharma class 10 maths.
chapter-16 question number-23 maths r d sharma,mensuration.

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1. Let the length of the pipe be h cm.

Then, Volume of cuboid = (53 x 40 x 15) cm3

Internal radius of the pipe = 7/2 cm = r

External radius of the pipe = 8/2 = 4 cm = R

So, the volume of iron in the pipe = (External Volume) – (Internal Volume)

= πR2h – πr2h

= πh(R2– r2)

= πh(R – r) (R + r)

= π(4 – 7/2) (4 + 7/2) x h

= π(1/2) (15/2) x h

Then from the question it’s understood that,

The volume of iron in the pipe = volume of iron in cuboid

π(1/2) (15/2) x h = 53 x 40 x 15

h = (53 x 40 x 15 x 7/22 x 2/15 x 2) cm

h = 2698 cm

Therefore, the length of the pipe is 2698 cm.

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