Question

The diameter of two circles are 28 cm and 24 cm. Find the circumference of the circle having its area equal to sum of the areas of the two circles.

Answer 1

Let R be the radius of the big circle.
The radii of two circles are

r₁ = `"d"_1/(2) = (28)/(2) = 14"cm"`

and 

r₂ = `"d"_2/(2) = (24)/(2) = 12"cm"`

Now,
Area of big circle
= Sum of areas of circles of radii r₁ and r₂
⇒ πR² = πr₁² + πr₂²
⇒ R² = r₁² + r₂²
⇒ R² = 14² + 12²
⇒ R² = 196 + 144
⇒ R² = 340
⇒ R = 18.4
∴ Circumference of big circle
= 2πR

= `2 xx (22)/(7) xx 18.4`
= 115.65cm².