Answer :
we have to find the radius, how can we got it??
[tex]C=2\pi*r[/tex]
then
[tex]40\pi=2\pi*r[/tex]
[tex]\boxed{r=20~cm}[/tex]
A quarter of the circle will have a surface of a quarter of the circle, there fore
this is the surface of the circle
[tex]S=\pi*r^2[/tex]
a quarter of it
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*r^2[/tex]
then we can replace the value of r
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*20^2[/tex]
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*400[/tex]
we can simplify
[tex]\boxed{\boxed{S_{\frac{1}{4}}=100\pi~cm^2}}[/tex]
[tex]C=2\pi*r[/tex]
then
[tex]40\pi=2\pi*r[/tex]
[tex]\boxed{r=20~cm}[/tex]
A quarter of the circle will have a surface of a quarter of the circle, there fore
this is the surface of the circle
[tex]S=\pi*r^2[/tex]
a quarter of it
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*r^2[/tex]
then we can replace the value of r
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*20^2[/tex]
[tex]S_{\frac{1}{4}}=\frac{1}{4}*\pi*400[/tex]
we can simplify
[tex]\boxed{\boxed{S_{\frac{1}{4}}=100\pi~cm^2}}[/tex]
[tex]2 \pi r=40 \pi \ cm\ \ \ \Rightarrow\ \ \ r= \frac{40 \pi }{2 \pi } =20\\\\S= \pi r^2\ \ \ \Rightarrow\ \ \ quarter:\ \ A= \frac{1}{4} \cdot S= \frac{1}{4} \cdot \pi \cdot20\cdot20=100 \pi \ [cm^2] [/tex]
