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Find 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. - Mathematics

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प्रश्न

Find 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.

योग

उत्तर

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

⇒ πR2 = π(r1)2 + π (r1)2

⇒ πR2 = π(24)2 + π(7)2

⇒ πR2 = 576π + 49π

⇒ πR2 = 625π

⇒ R2 = 625

⇒ R = 25

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

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