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joja
2 months ago
13

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.
Mathematics
1 answer:
zzz [12.3K]2 months ago
4 0
The expression is 4*sqrt(30). Work Shown: Let's define circles P and Q with P representing the area of the circle with a radius of 19 and Q for a radius of 29. By using A = π*r², P calculates to 361π and Q to 841π. The resultant shaded area between circles P and Q is R = Q - P, which amounts to 480π. To ascertain the radius of a new circle S that would equal this area, we simplify R = 480π to find r = sqrt(480) leading us to r = 4*sqrt(30).
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