Question

If the circumference of the circle increases from 2 to 4.Then its area is -----------

Answer 1

Answer:

the area of the circle increases from

$\frac{1}{\pi} \:square\:units\:to\:\frac{4}{\pi} \:square\:units$

Step-by-step explanation:

Formula used:

circumference of circle having radius r

$=2\:{\pi}r$

Area of a circle having radius 'r' is $\pi\:r^2$ square units

$when\\circumference = 2\\\\2\:{\pi}r_1=2\\\\\pi\:r_1=1\\\\r_1=\frac{1}{\pi}$

Area of the circle

$=\pi\:r_{1}^2\\\\=\pi\:(\frac{1}{\pi})^2\\\\=\pi\:(\frac{1}{\pi}^2)\\\\=\frac{1}{\pi} \:square\:units$

$when\\circumference = 4\\\\2\:{\pi}r_2=4\\\\\pi\:r_2=2\\\\r_2=\frac{2}{\pi}$

Area of the circle

$=\pi\:r_{2}^2\\\\=\pi\:(\frac{2}{\pi})^2\\\\=\pi\:(\frac{4}{\pi}^2)\\\\=\frac{4}{\pi} \:square\:units$

Therefore

the area of the circle increases from

$\frac{1}{\pi} \:square\:units\:to\:\frac{4}{\pi} \:square\:units$

Answer 2

Answer:

Area become 4 times

Step-by-step explanation:

If the circumference of the circle increases from 2 to 4.Then its area is -----------

Circumference ∝ Radius

circumference become from 2 to 4

=> circumference is doubled

if circumference is doubled it means radius is doubled

Area ∝ Radius²

radius is doubled   2² = 4

=> Area become 4 times