Mathematics
The radius of a circle whose area is equal to the sum of the areas of two circles of radii 7 cm and 24 cm respectively is :
31 cm
28 cm
27 cm
25 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.(7)2 = 49π.
⇒ A2 = π.(24)2 = 576π
∴ Sum of the areas of the two circles = 49π + 576π = 625π.
Let the radius of new circle be 'R' cm.
⇒ πR2 = 625π
⇒ R2 = 625
⇒ R = = 25 cm.
Hence, option 4 is the correct option.
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