Question

if the circumference of a circle increases from 4 pi to 8 pi, find the percentage increase in the area of a circle​

Answer 1

$\fontsize{18}{10}{\textup{\textbf{Area is increased by 300 percent.}}}$

Step-by-step explanation:

Let r units and r' units denote the radius of the given circle with circumference 4π and 8π respectively.

Then, we have

$2\pi r=4\pi\\\\\Rightarrow r=\dfrac{4\pi}{2\pi}\\\\\Rightarrow r=2$

and

$2\pi r^\prime=8\pi\\\\\Rightarrow r^\prime=\dfrac{8\pi}{2\pi}\\\\\Rightarrow r^\prime=4$

Now, the area of the circle with radius 2 units is

$A_1=\pi r^2=\pi \times2^2=4\pi$

and the area of the circle with radius 4 units is

$A_2=\pi (r^\prime)^2=\pi \times4^2=16\pi$

Therefore, the percent increase in the area of the circle is

$\dfrac{A_2-A_1}{A_1}\times100\%\\\\\\=\dfrac{16\pi-4\pi}{4\pi}\times100\%\\\\=\dfrac{12\pi}{4\pi}\times100\%\\\\=300\%.$

Thus, the area of the circle is increased by 300%.

#Learn more

Question :  If the radius of the circle is increased by 100%, by what percent is the area of the circle increased?

Link : https://brainly.in/question/2694229.