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Question
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 ______.
Options
31 cm
25 cm
62 cm
50 cm
Solution
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 50 cm.
Explanation:
Let r1 = 24 cm and r2 = 7 cm
∴ Area of first circle = `π"r"_1^2`
= π(24)2
= 576π cm2
And area of second circle = `π"r"_2^2`
= π(7)2
= 49π cm2
According to the given condition,
Area of circle = Area of first circle + Area of second circle
∴ πR2 = 576π + 49π ...[Where, R be radius of circle]
⇒ R2 = 625
⇒ R = 25 cm
∴ Diameter of a circle = 2R
= 2 × 25
= 50 cm
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