Surface Areas and Volumes · Class 9 · CBSE Mathematics

If the radius of a sphere is doubled, how many times does its volume increase?

Practice question from Surface Areas and Volumes (Class 9 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-CA95FD

If the radius of a sphere is doubled, how many times does its volume increase?

  1. A.2 times
  2. B.4 times
  3. C.8 timesCorrect answer
  4. D.16 times

Solution

The volume of a sphere is given by V=43πr3V = \frac{4}{3}\pi r^3. If rr is replaced by 2r2r, the new volume becomes 43π(2r)3=8×(43πr3)\frac{4}{3}\pi (2r)^3 = 8 \times \left(\frac{4}{3}\pi r^3\right), which is 8 times the original volume.

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