Question

The area of a circle is given by the formula A=πr^2, and the circumference of the circle is given by C=2πr. Find the ratio of the area to the circumference. What happens to this ratio as the radius is quadrupled?

Answer 1

\[
\frac {\pi r^2}{2 \pi r}=\frac r 2
\]

Answer 2

so if the radius is quadrupled, then it would be 4r/8?

Answer 3

\[\frac{ pi r^2}{2 pi r }\]
\[\frac{ pi (4r)^2}{2 pi(4 r)}=\frac{16pi r^2}{8 pi r}\]

Answer 4

oh ok

Answer 5

So compare the coefficients. The first one is 1/2 . After quadrupling the radius, the coefficient is 2. What do you do to 1/2 to get 2?

Answer 6

Clearly 1/2 times 4 is 2 so quadrupling the radius also quadrupled the ratio.