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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration
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The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the original cylinder?
Solution:
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it.
Let the radius of the base of a right circular cylinder be r and height be h.
Volume of the cylinder, V1 = π r2h
The radius of the base of a right circular cylinder is halved and the height is doubled.
So radius of new cylinder = r/2
Height of new cylinder = 2h
Volume of the new cylinder, V2 = π r2h
= π (r/2)2 ×2h
= ½ π r2h
So ratio of volume of new cylinder to the original cylinder , V2/V1= ½π r2h/π r2h = ½
Hence the required ratio is 1:2.
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