Multiple choice

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?

  1. 12 cm and 5 cm

  2. 24 cm and 10 cm

  3. 60 cm and 25 cm

  4. 30 cm and 12.5 cm

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let radii be 12k and 5k (diameter ratio 12:5). Sum of areas: π(12k)² + π(5k)² = π(144k² + 25k²) = 169πk². Target circle area: π(32.5)² = 1056.25π. Equating: 169k² = 1056.25, so k² = 6.25 and k = 2.5. Therefore radii are 12×2.5 = 30 cm and 5×2.5 = 12.5 cm. Note that options A and B show diameters, not radii.