Surface Areas and Volumes · Class 10 · CBSE Mathematics

If the radius of the base of a right circular cylinder is halved, keeping the height the same, the ratio of the volume of the reduced cylinder to tha…

Practice question from Surface Areas and Volumes (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-7F97CF

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

  1. A.1 : 2
  2. B.1 : 4Correct answer
  3. C.1 : 8
  4. D.2 : 1

Solution

The volume of a cylinder is given by V=πr2hV = \pi r^2 h. If the radius becomes r/2r/2 and height remains hh, the new volume is V′=π(r/2)2h=14πr2hV' = \pi (r/2)^2 h = \frac{1}{4} \pi r^2 h. Thus, the ratio V′:VV' : V is 1:41 : 4.

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