Multiple choice

The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area?

  1. 300%

  2. 400%

  3. 450%

  4. 500%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume V is proportional to r^3, so an 800% increase in volume (V_new = 8V_old) means the radius increases by a factor of 2 (since 2^3 = 8). Surface area A is proportional to r^2, so the new area is 2^2 = 4 times the original area, which is a 300% increase.

AI explanation

An increase of 700% in volume means the new volume is 800% of the original, so the ratio of the new volume to the old volume is 8. Because the radius is the cube root of 8, the radius doubles, and the surface area, being proportional to the square of the radius, becomes four times the original area. Since four times the original area represents a 300% increase over the initial area, the percentage increase in surface area is 300%.

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