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.

Given:

Let the two circles with radii 4 cm and 3 cm be C_{1} and C_{2} respectively.

⇒ r_{1} = 4 cm and r_{2} = 3 cm

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

∵ Area of circle = πr^{2} …… (ii)

∴ Area of C_{1} = πr_{1}^{2}

=

= × 16 = cm^{2}

Similarly, Area of C_{2} = πr_{2}^{2}

= × 3 × 3

= × 9 = cm^{2}

So, using (i), we have

Area of C = + = cm^{2}

Now, using (ii), we have

πr^{2} =

× r^{2} =

r^{2} = × = 25

r = √25 = 5

r = 5 cm

∵ Diameter = 2 × radius

∴ Diameter = 2 × 5 = 10 cm

__Hence, diameter of the circle with area equal to the sum of two circles of radii 4 cm and 3cm is 10 cm.__

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