radius - r
area:
\(A_1=\pi r^2\)
circumference:
\(C_1=2 \pi r\)
the length of the radius is doubled
radius - 2r
area:
\(A_2=\pi \times (2r)^2=\pi \times 4r^2=4 \pi r^2\)
circumference:
\(C_2=2 \pi \times 2r=4 \pi r\)
\(\frac{A_2}{A_1}=\frac{4 \pi r^2}{\pi r^2}=4 \\ \\
\frac{C_2}{C_1}=\frac{4 \pi r}{2 \pi r}=\frac{4}{2}=2\)
When the length of the radius is doubled, the area is quadrupled and the circumference is doubled.
