Multiple choice

If the radius of a hemisphere is increased by 25%, what would be the percentage increase in its total surface area?

  1. 48.5%

  2. 60%

  3. 56.25%

  4. 72%

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Surface area of a hemisphere is 3*pi*r^2. If r increases by 25% (1.25r), the new area is 3*pi*(1.25r)^2 = 3*pi*1.5625*r^2. The increase is 56.25%.

AI explanation

The total surface area of a hemisphere formula is 3 times pi times r squared, so the area depends on the square of the radius. If the radius is increased by 25%, the new radius becomes 1.25 times the original, and squaring 1.25 gives 1.5625. This means the new surface area is 56.25% larger than the original area.

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