Question

The circle will be enlarged by a scale factor of 4.

Answer 1

Answer:

The area of the new circle is  $144\pi \ in^2$

Step-by-step explanation:

Given:

radius of the circle = 3 in.

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared.

Let

z-----> the scale factor

x-----> the area of the enlarged circle

y-----> the area of the original circle

So;

$z^2= \frac{x}{y}$

In this problem we have

$z=4$ ----> the scale factor

The area of the original circle is equal to

$y = \pi r^2= \pi (3)^2= 9\pi \ in^2$

Now substituting value of y and solve for x we get;

$4^2=\frac{x}{9\pi}\\ \\x= 16\times9\pi= 144\pi \ in^2$

Hence Area of the new Circle is $144\pi \ in^2$

Also The area of the enlarged circle is 16 times the area of the original circle.