2020 · Q90
Let PQRS be the diameter of a circle of radius 9 cm. The length PQ, QR and RS are equal. Semi-circle is drawn with QS as diameter (as shown in the given figure). What is the ratio of the shaded region to that of the unshaded region?
Elementary MathematicsCircles
- A25 : 121
- B5 : 13
- C5 : 18
- D1 : 2
Explanation
The shaded region is the upper half-disc of radius 9 minus the semicircle on QS of radius 6: ½π(81 − 36) = 22.5π. The unshaded part of the big circle is 81π − 22.5π = 58.5π. Ratio = 22.5 : 58.5 = 5 : 13.