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Question
The area of circle is equal to the sum of the areas of two circles of radii 24 cm and 7 cm. The diameter of the new circle is
Options
25 cm
31 cm
50 cm
62 cm
Solution
50 cm
Let r cm be the radius of the new circle.
Now,
Area of the new circle = Area of the circle with radius 24 cm + Area of the circle with radius 7 cm
Thus, we have:
`πr^2 = pi"r"_1^2 + pi"r"_2^2`
`=> pi"r"^2=[pixx(24)^2+pixx(7)^2]"cm"^2`
`=>pi"r"^2 = [pixx576+pixx49]"cm"^2`
`=>pi"r"^2 = pixx(576+49) "cm"^2`
`=> "r"^2 = 625 pi "cm"^2`
`=>"r"^2 = 625`
`=> "r" = 25`
∴ Diameter of the new circle = (25 × 2) cm
= 50 cm
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