Question

Circumference of a circle is 40 π cm. A quarter of the circle represents the developer layer genuine coupe. Calculate the surface compartment.

Answer 1

`2 \pi r=40 \pi \ cm\ \ \ \Rightarrow\ \ \ r= (40 \pi )/(2 \pi ) =20\\\\S= \pi r^2\ \ \ \Rightarrow\ \ \ quarter:\ \ A= (1)/(4) \cdot S= (1)/(4) \cdot \pi \cdot20\cdot20=100 \pi \ [cm^2]`

Answer 2

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_{(1)/(4)}=(1)/(4)*\pi*r^2`

then we can replace the value of r


`S_{(1)/(4)}=(1)/(4)*\pi*20^2`


`S_{(1)/(4)}=(1)/(4)*\pi*400`

we can simplify


`\boxed{\boxed{S_{(1)/(4)}=100\pi~cm^2}}`