Question

How will the area of the circle change if it is dilated by a scale factor of 1/2

Answer 1

The circle would get smaller.

Answer 2

Answer:  The area of the dilated circle will be one-forth of the area of the original circle.

Step-by-step explanation:  We are given to find the change in area of a circle if it is dilated by a scale factor of half.

Let r represents the RADIUS and A represents the AREA of the circle before dilation.

And, r' represents the radius and A' represents the AREA of the circle after dilation.

So, we get

$A=\pi r^2~~~~~~\textup{and}~~~~~~A'=\pi r'^2.$

In case of a circle, scale factor is the ratio of the radius of the dilated circle to the radius of the original circle.

That is,

$\dfrac{1}{2}=\dfrac{r'}{r}\\\\\\\Rightarrow r'=\dfrac{r}{2}.$

Therefore, the area of the dilated circle will be

$A'=\pi r'^2=\pi \times\left(\dfrac{r}{2}\right)^2=\dfrac{\pi r^2}{4}=\dfrac{1}{4}\times A.$

Thus, the area of the dilated circle will be one-forth of the area of the original circle.