Question

Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.

Answer 1

Let R be the radius of the big circle.
The radii of two circles are r₁ = 3cm and r₂ = 4cm
Now,
Circumference of big circle
= Sum of circumference of circles of radii r₁ and r₂
⇒ 2πR = 2πr₁ + 2πr₂
⇒ R = r₁ + r₂
⇒ R
= 3 + 4
= 7cm
∴ Area of big circle

= πR² = `(22)/(7) xx 7 xx 7` 
= 154cm².