Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

prealgebra senior

Problem

Two concentric circles with radii of 19 and 29 units bound a shaded region. A third circle will be drawn with area equal to that of the shaded area. What must the radius of the third circle be? Express your answer in simplest radical form.

problem
Solution
Since the shaded region is everything inside the larger circle but outside the smaller, its area is . So, letting the radius of the third circle be , we have , or .
Final answer
4\sqrt{30}