Question

Please help with this question!! I need serious help!!

Answer 1

Answer:

The circumference is multipled by 4.

Step-by-step explanation:

The formula of an area of a circle"

$A=\pi r^2$

The formula of a circumference of a circle:

$C=2\pi r$

The area multipled by 16:

$16A=16\pi r^2\\\\16A=\pi(4^2r^2)\\\\16A=\pi(4r)^2$

The radius has increased fourfold, therefore:

$C'=2\pi(4r)=4(2\pi r)=4C$

The circumference is multipled by 4.

You can calculate the area and check the circumference:

$r=11.6\ in\\\\A=\pi(11.6)^2=132.56\pi\\\\16A=(16)(134.56\pi)=2152.96\pi\ in^2$

Calculate the radius:

$\pi r^2=2152.96\pi$             divide both sides by π

$r^2=2152.96\to r=\sqrt{2152.96}\\\\r=46.4\ in$

Calculate the circumference of both circles:

$r=11.6\ in\\\\C=2\pi(11.6)=23.2\pi\ in$

$r=46.4\ in\\\\C'=2\pi(46.4)=92.8\pi\ in$

$\dfrac{C'}{C}=\dfrac{92.8\pi}{23.2\pi}=4\to C'=4C$