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.
Deepak BoraNewbie
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.
Share
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 = (R2-r2)h
= ×(52-32)×h
= h(25-9)
= 16h cm3
Let r be the radius of solid cylinder.
Volume of solid cylinder = r2h
Since pipe is melted and changed into a cylinder, their volumes remains same.
r2h = 16h
r2 = 16
r = 4 cm
Diameter = 2r = 2×4 = 8 cm
Hence the diameter of the cylinder is 8 cm.