Multiple choice

If the volume in $ \displaystyle m ^{2} $ and the surface area in $ \displaystyle m ^{2} $ of a sphere are numerically equal then the radius of the sphere in m is

  1. 4

  2. 2

  3. 3.5

  4. 3
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D Correct answer
Explanation

The volume of a sphere is 4/3 pi r^3 and its surface area is 4 pi r^2. Equating their numerical values gives 4/3 pi r^3 = 4 pi r^2, so r = 3 m, with r = 0 excluded.

AI explanation

The formula for the volume of a sphere is (4/3) * pi * r^3 and the formula for its surface area is 4 * pi * r^2. Equating the two numerical values gives (4/3) * pi * r^3 = 4 * pi * r^2. Dividing both sides by 4 * pi * r^2 yields r / 3 = 1, so the radius is 3 m.

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