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) – (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
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.