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Question
What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?
Solution
Let the diameter of the required circle be d.
Now, Area of required circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm
`=>pi("d"/2)^2 = pi(10/2)^2 + pi(24/2)^2`
`=> ("d"/2)^2 = 25+144`
`=> ("d"/2)^2 = 13^2`
`=> "d"/2 = 13`
`=> d = 26 "cm"`
Hence, the diameter of the circle is 26 cm.
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