Question

The radii of two circles are 3cm and 4cm. Find the radius of a circle whose area is equal to the sum

Answer 1

Answer:

Given, the radius of the two circles are 3 cm and 4 cm  

Then the area of the circle whose radius is 4 cm =$\pi r^{2}$

                                                                                 =$\pi (4)^{2}$

                                                                                 =16π sq cm

And the area of the circle whose radius is 3 cm =$\pi r^{2}$

                                                                               =$\pi (3)^{2}$

                                                                               =9πsq cm  

Then the area of a circle whose area is equal to the sum of both circles=16π+9π=25π sq cm  

Let the radius of the new circle is R cm

∴$\pi R^{2} = 25\pi$

⇒ $R^{2} = 25$

⇒$R = 5 cm$

So the radius of the new circle =5 cm.

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