What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameter 10 cm and 24 cm?

Given:

Let the two circles be C_{1} and C_{2} with diameters 10 cm and 24 cm respectively.

Area of circle, C = Area of C_{1} + Area of C_{2} …… (i)

∵ Diameter = 2 × radius

∴ Radius of C_{1}, r_{1} = = 5 cm

and Radius of C_{2}, r_{2} = = 12 cm

∵ Area of circle = πr^{2} …… (ii)

∴ Area of C_{1} = πr_{1}^{2}

=

=

= cm^{2}

Similarly, Area of C_{2} = πr_{2}^{2}

=

= 22/7 × 144

= cm^{2}

∴ Using equation (i), we have

Area of C = +

= cm^{2}

Now, using equation (ii), we have

× r^{2} =

r^{2} =

r^{2} = 169

r =

r = 13 cm

⇒ Diameter = 2 × r

= 2 × 13

= 26 cm

__Hence, the diameter of the circle is 26 cm.__

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