we have to find the radius, how can we got it??
\(C=2\pi*r\)
then
\(40\pi=2\pi*r\)
\(\boxed{r=20~cm}\)
A quarter of the circle will have a surface of a quarter of the circle, there fore
this is the surface of the circle
\(S=\pi*r^2\)
a quarter of it
\(S_{\frac{1}{4}}=\frac{1}{4}*\pi*r^2\)
then we can replace the value of r
\(S_{\frac{1}{4}}=\frac{1}{4}*\pi*20^2\)
\(S_{\frac{1}{4}}=\frac{1}{4}*\pi*400\)
we can simplify
\(\boxed{\boxed{S_{\frac{1}{4}}=100\pi~cm^2}}\)
