Answer: d.) The area of the new circle is 16 times larger.
Step-by-step explanation:
Let the radius of the original circle be r.
Then the area of the original circle will be :-
[tex]\text{A}_1=\pi r^2[/tex]
When she multiplies her original radius by four and repaints the circle.
The new radius = [tex]R=4r[/tex]
Then the area of the new circle will be :-
[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]
Hence, The area of the new circle is 16 times larger.
