Answer:
The area of the new circle is [tex]144\pi \ in^2[/tex]
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;
[tex]z^2= \frac{x}{y}[/tex]
In this problem we have
[tex]z=4[/tex] ----> the scale factor
The area of the original circle is equal to
[tex]y = \pi r^2= \pi (3)^2= 9\pi \ in^2[/tex]
Now substituting value of y and solve for x we get;
[tex]4^2=\frac{x}{9\pi}\\ \\x= 16\times9\pi= 144\pi \ in^2[/tex]
Hence Area of the new Circle is [tex]144\pi \ in^2[/tex]
Also The area of the enlarged circle is 16 times the area of the original circle.
