ICSE Board Question Based on Mensuration Chapter of M.L Aggarwal for class10

In this question the radius of the base of a right circular cylinder is halved and the height is doubled. What will be the ratio of the volume of the new cylinder to that of the original cylinder?

This is the Question Number 13, Exercise 17.1 of M.L Aggarwal.

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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?

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This answer was edited.Let the radius of the base of a right circular cylinder be r and height be h.Volume of the cylinder, V_{1}= πr^{2}hThe radius of the base of a right circular cylinder is halved and the height is doubled.So radius of new cylinder = r/2Height of new cylinder = 2hVolume of the new cylinder, V_{2}= πr^{2}h= π(r/2)^{2 }×2h= ½ πr^{2}hSo ratio of volume of new cylinder to the original cylinder , V_{2}/V_{1}= ½ πr^{2}h/πr^{2}h = ½Hence the required ratio is 1:2.