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The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 

A. 31 cm  B. 25 cm C. 62 cm D. 50 cm

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D. 50 cm

Area of first circle = πr2 = π(24)2 = 576π m2

Area of second circle = πr2 = π(7)2 = 49π m2

Now, we are given that,

Area of the circle = Area of first circle + Area of second circle

∴ πR2 = 576π +49π

(where, R is the radius of the new circle)

⇒ πR2 = 625π

⇒ R2 = 625

⇒ R = 25

∴ Radius of the circle = 25cm

Thus, diameter of the circle = 2R = 50 cm.

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