Multiple choice

The difference between the radii of the smaller circle and the bigger circle is $7 cm$ and the difference between the areas of the two circles is $1078$ sq cm. What is the radius of the smaller circle in cm?

  1. $28$
  2. $21$
  3. $17.5$
  4. $35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let R and r be the radii. R - r = 7. pi * (R^2 - r^2) = 1078. pi * (R - r)(R + r) = 1078. (22/7) * 7 * (R + r) = 1078. R + r = 49. Solving R - r = 7 and R + r = 49 gives 2R = 56, R = 28, r = 21.

AI explanation

Let the radius of the smaller circle be r, making the radius of the bigger circle r plus 7. The difference between their areas is given by the area formula pi times R squared minus pi times r squared, which equals 1078. Substituting R gives pi multiplied by the quantity r plus 7 squared minus pi times r squared equals 1078, simplifying to pi times 14r plus 49 equals 1078. Using the approximation of pi as 22 divided by 7, the equation becomes 22 divided by 7 multiplied by 14r plus 49 equals 1078, which solves to 44r plus 154 equals 1078, yielding a radius of 21 cm for the smaller circle.

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