Question

The circumference of a circle is 6.28. What is the area of the circle

Answer 1

\[\large C = 2\pi r\]
\[\large A = \pi r^2\]

Notice there is an 'r' in each equation...lets solve the top one for 'r'

\[\large r = \frac{C}{2\pi}\]

Now lets substitute that into the 2nd equation for 'r'

\[\large A = \pi(\frac{C}{2\pi})^2\]
\[\large A = \pi(\frac{C^2}{4\pi^2})\]
\[\large A=\frac{\cancel{\pi} C^2}{4\pi\cancel{^2}}\]
\[\large A = \frac{C^2}{4\pi}\]
Now lets substitute the fact that we know C = 6.28
\[\large A = \frac{(6.28)^2}{4\pi}\]
\[\large A = \frac{39.4384}{12.56}\]
\[\large A = 3.14 = \pi \]