Multiple choice

If the radius of a circle is increased by 29%, then its area increases by

  1. 58%

  2. 29%

  3. 33.205%

  4. 66.41%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If radius r increases by 29%, the new radius is 1.29r. The new area is pi * (1.29r)^2 = pi * 1.6641 * r^2. The increase is 1.6641 - 1 = 0.6641, or 66.41%.

AI explanation

Let the original radius be 100, so the new radius after a 29 percent increase is 129. The original area of the circle is pi multiplied by the square of 100, and the new area is pi multiplied by the square of 129. The percentage increase is found by the formula new area minus old area divided by old area and multiplied by 100, which simplifies to 6641 divided by 100 to equal 66.41 percent.

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