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