Multiple choice

The sum of the radii of the two circles is 91 cm and the difference between their area is 2002 cm2. What is the radius (in cm) of the larger circle?

  1. 56

  2. 42

  3. 63

  4. 49
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D Correct answer
Explanation

Let R and r be the radii. R + r = 91 and pi(R^2 - r^2) = 2002. Since R^2 - r^2 = (R-r)(R+r), we have 2002/pi = (R-r)*91. Using pi = 22/7, 2002 * 7 / 22 = 637. So (R-r) = 637 / 91 = 7. Solving R+r=91 and R-r=7 gives 2R = 98, so R = 49.

AI explanation

Let the radii be R and r, so R + r = 91. The difference in their areas is pi * (R^2 - r^2) = 2002, which factors using the difference of squares into pi * (R + r) * (R - r) = 2002. Substituting R + r = 91 and pi = 22/7 gives (22/7) * 91 * (R - r) = 2002, which simplifies to R - r = 7. Solving the two equations yields the larger radius R = 49 cm.

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