Question

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm.

Answer 1

Let the diameter of the required circle be d.

Now, of the required circle = Are of circle having 4 cm + Area of circle having radius 3 cm

`⇒pi("d"/2)^2=pi(4)^2+pi(3)^2`

`=>("d"/2)^2 = 16 + 9`

`=>("d"/2)^2 = 25 =(5)^2`

`=>"d"/2 = 5`

⇒ d = 10 cm

Hence, the diameter of the circle is 10 cm.