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.

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) â€“ (Internal Volume)

= Ï€R2h â€“ Ï€r2h

= Ï€h(R2â€“ r2)

= Ï€h(R â€“ r) (R + r)

= Ï€(4 â€“ 7/2) (4 + 7/2) x h

= Ï€(1/2) (15/2) x h

Then from the question itâ€™s understood that,

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

Ï€(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.