Multiple choice

If the radius of the sphere is halved, what will be the change in its surface area?

  1. $1/4^{th}$
  2. $1/3^{rd}$
  3. $1/6^{th}$
  4. $1/9^{th}$
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A Correct answer
Explanation

Surface area of a sphere is 4 * pi * r^2. If the radius is halved (r/2), the new surface area is 4 * pi * (r/2)^2 = 4 * pi * (r^2 / 4) = (1/4) * (4 * pi * r^2). The area becomes 1/4 of the original.

AI explanation

Surface area is directly proportional to the square of the radius. If the radius is halved, the new radius becomes r/2, making the new surface area 4 times pi times (r/2) squared. The new area equals 1/4 of the original surface area, so it becomes 1/4th.

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