Multiple choice

The radii of two circles are $48:cm$ and $13: cm$. Find the area of the circle which has its circumference equal to the difference of the circumferences of the given two circles.

  1. $3850 \: cm^{2}$
  2. $2850 \: cm^{2}$
  3. $1850 \: cm^{2}$
  4. $4850 \: cm^{2}$
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A Correct answer
Explanation

Circumference 1 = 2*pi*48, Circumference 2 = 2*pi*13. Difference = 2*pi*(48-13) = 2*pi*35. New circle circumference = 2*pi*r = 2*pi*35, so r = 35. Area = pi * 35^2 = 1225 * 22/7 = 3850.

AI explanation

The difference in the circumferences of the two circles gives 2 times pi times 48 minus 2 times pi times 13, which equals 2 times pi times 35. This makes the radius of the new circle 35 cm. Applying the area of a circle formula, Area = pi times r squared, we calculate 22/7 times 35 times 35, resulting in 3850 square cm.

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