ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 11 Mensuration Exercise 17.5

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.



When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

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 =π (R2-r2)h

= π (52-32)×h

= π h(25-9)

= 16π h cm3

Let r be the radius of solid cylinder.

Volume of solid cylinder = π r2h

Since pipe is melted and changed into a cylinder, their volumes remains same.

π r2h = 16π h

r2 = 16

r = 4 cm

Diameter = 2r = 2×4 = 8 cm

Hence the diameter of the cylinder is 8 cm.

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