Mathematics
The radius of the circle whose area is equal to the sum of areas of two circles of radii 9 cm and 12 cm respectively is :
11 cm
12 cm
14 cm
15 cm
Mensuration
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Answer
Let A1 and A2 be the areas of two circles.
Area = πr2
Areas of the two circles:
⇒ A1 = π.(9)2 = 81π.
⇒ A2 = π.(12)2 = 144π
∴ Sum of the areas of the two circles = 81π + 144π = 225π.
Let the radius of new circle be R cm.
⇒ πR2 = 225π
⇒ R2 = 225
⇒ R = = 15 cm.
Hence, option 4 is the correct option.
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