M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.

A hollow copper pipe of inner diameter and outer diameter are given is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

This is the Question Number 10, Exercise 17.5 of M.L Aggarwal.

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# A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

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Given inner diameter of the pipe = 6 cm

So inner radius, r = 6/2 = 3 cm

Outer diameter = 10 cm

Outer radius, R = 10/2 = 5 cm

Let h be the height of the pipe.

Volume of pipe = (R

^{2}-r^{2})h= Ã—(5

^{2}-3^{2})Ã—h= h(25-9)

= 16h cm

^{3}Let r be the radius of solid cylinder.

Volume of solid cylinder = r

^{2}hSince pipe is melted and changed into a cylinder, their volumes remains same.

r

^{2}h = 16hr

^{2Â }= 16r = 4 cm

Diameter = 2r = 2Ã—4 = 8 cm

Hence the diameter of the cylinder is 8 cm.