Answer:
The circumference is multipled by 4.
Step-by-step explanation:
The formula of an area of a circle"
[tex]A=\pi r^2[/tex]
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
The area multipled by 16:
[tex]16A=16\pi r^2\\\\16A=\pi(4^2r^2)\\\\16A=\pi(4r)^2[/tex]
The radius has increased fourfold, therefore:
[tex]C'=2\pi(4r)=4(2\pi r)=4C[/tex]
The circumference is multipled by 4.
You can calculate the area and check the circumference:
[tex]r=11.6\ in\\\\A=\pi(11.6)^2=132.56\pi\\\\16A=(16)(134.56\pi)=2152.96\pi\ in^2[/tex]
Calculate the radius:
[tex]\pi r^2=2152.96\pi[/tex] divide both sides by π
[tex]r^2=2152.96\to r=\sqrt{2152.96}\\\\r=46.4\ in[/tex]
Calculate the circumference of both circles:
[tex]r=11.6\ in\\\\C=2\pi(11.6)=23.2\pi\ in[/tex]
[tex]r=46.4\ in\\\\C'=2\pi(46.4)=92.8\pi\ in[/tex]
[tex]\dfrac{C'}{C}=\dfrac{92.8\pi}{23.2\pi}=4\to C'=4C[/tex]
