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Question

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:


  1. 1 : 4

  2. 4 : 1

  3. 1 : 2

  4. 2 : 1


Solution

The correct option is A

1 : 4


Let the radius and height of the original cylinder be r and h respectivley.
Volume of the orignal cylinder =πr2h
According to the question, radius of the new cylinder is halved keeping the height same.
Radius of the new cylinder =r2
Also, height of the new cylinder =h
Volume of the new cylinder =π(r2)2h=πr2h4
Volume of the new cylinderVolume of the original cylinder=(πr2h4)(πr2h)=(14)=1:4

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