2017 · Q56
The diameters of two given circles are in the ratio 12 : 5 and the sum of their areas is equal to the area of a circle of diameter 65 cm. What are their radii ?
Elementary MathematicsCircles
- A12 cm and 5 cm
- B24 cm and 10 cm
- C60 cm and 25 cm
- D30 cm and 12.5 cm
Explanation
Let the radii be 12k and 5k. Then π(12k)²+π(5k)² = π(65/2)², i.e. 169k² = 4225/4, so k² = 25/4 and k = 2.5. The radii are 30 cm and 12.5 cm. Hence option (D) 30 cm and 12.5 cm.