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