Multiple choice

If the radius of a circle is increased by 31%, its area increases by ______.

  1. 62%

  2. 31%

  3. 35.805%

  4. 71.61%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If radius r increases by 31%, the new radius is 1.31r. The new area is pi*(1.31r)^2 = 1.7161 * pi*r^2. The increase is 71.61%.

AI explanation

Using the area of a circle formula A = pi * r^2, if the new radius is 1.31r, the new area becomes pi * (1.31r)^2 = 1.7161 * pi * r^2. This shows the new area is 171.61% of the original area. The percentage increase in area is 171.61 - 100 = 71.61%.

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