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 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.