Question

If the radius of the circle is multiplied by a factor of 3, then the area of the circle is multiplied by a factor of

Answer 1

$\bf \textit{area of a circle}\\\\ A=\pi r^2\quad \begin{cases} r=radius\\ -----\\ r=\stackrel{r\times 3}{3r} \end{cases}\implies A=\pi (3r)^2 \\\\\\ A=\pi (3^2r^2)\implies A=9(\pi r^2)$

notice, if the original area was πr², then the new area has a factor in front of it, that much.