Answer:
The area of the new circle is [tex]144 \pi\ in^{2}[/tex]
Step-by-step explanation:
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]
substitute and solve for x
[tex]4^{2} =\frac{x}{9\pi}[/tex]
[tex]x=16*9 \pi=144 \pi\ in^{2}[/tex]
The area of the enlarged circle is [tex]16[/tex] times the area of the original circle
