Answer :

Given:

Let the two circles with radii 4 cm and 3 cm be C1 and C2 respectively.


r1 = 4 cm and r2 = 3 cm


Area of circle, C = Area of C1 + Area of C2 …… (i)


Area of circle = πr2 …… (ii)


Area of C1 = πr12


=


= × 16 = cm2


Similarly, Area of C2 = πr22


= × 3 × 3


= × 9 = cm2


So, using (i), we have


Area of C = + = cm2


Now, using (ii), we have


πr2 =


× r2 =


r2 = × = 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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