**Question Statement:**
If the circumference of a circle is increased by 20%, then the area of the circle will be increased by:

Question

**Question Statement:**  
If the circumference of a circle is increased by 20%, then the area of the circle will be increased by:

Accepted Answer

Let the initial radius of the circle be $$ r_0 $$. The circumference of the circle is given by $$ 2\pi r_0 $$. If the circumference increases by 20%, the new circumference becomes:

$$
2\pi r_n = 2\pi r_0 	imes \frac{6}{5}
$$

This implies:  
$$
r_n = r_0 	imes \frac{6}{5}
$$

The area of a circle is $$ \pi r^2 $$. The old area is:  
$$
	ext{Old Area} = \pi r_0^2
$$

The new area is:  
$$
	ext{New Area} = \pi r_n^2 = \pi \left(r_0 	imes \frac{6}{5}ight)^2 = \pi r_0^2 	imes \frac{36}{25}
$$

The percentage increase in area is:  
$$
	ext{Increase} = \left(\frac{	ext{New Area} - 	ext{Old Area}}{	ext{Old Area}}ight) 	imes 100
= \left(\frac{\pi r_0^2 	imes \frac{36}{25} - \pi r_0^2}{\pi r_0^2}ight) 	imes 100
= \left(\frac{\frac{36}{25} - 1}{1}ight) 	imes 100
= \left(\frac{11}{25}ight) 	imes 100 = 44\%
$$

Thus, the area of the circle increases by **44%**.

Answer

Answer

Answer