The radius of a circle is increased so that its circumference increases by 15%

• Mensuration

The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by

1. 31.25%
2. 32.25%
3. 33.25%
4. 34.25%

Answer

Circumference of circle = 2πr

Area of circle = πr²

New circumference after increase in radius = 1.15 × 2πR

Since circumference ∝ radius of circle, radius increases by 15%

R = 1.15r

New Area = πR² = π(1.15r)² = 1.3225πr²

So, area is increased by 32.25%.

The correct option is B.