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?

Answer 1

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.