Multiple choice

The volume of a sphere of radius r is obtained by multiplying its surface area by

  1. r/3

  2. 3r

  3. 4r/3

  4. 4/3

  5. None of these
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A Correct answer
Explanation

The volume of a sphere is (4/3) * pi * r^3 and the surface area is 4 * pi * r^2. Dividing the volume by the surface area gives ((4/3) * pi * r^3) / (4 * pi * r^2) = r/3.

AI explanation

The surface area of a sphere with radius r is given by the formula 4 times pi times r squared. The volume of the sphere is given by the formula 4 thirds times pi times r cubed. If you multiply the surface area by r divided by 3, you get 4 times pi times r squared times r divided by 3, which simplifies exactly to the volume formula. Therefore, the necessary multiplier is r/3.

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