exercise - differentiation application questions

1

The figure is a gym.

The perimeter is 400 m and encloses an area of $A$ $m^2$.

1a

Show that the area enclosed by the track is given by $A=400r-\pi r^2$

We know that $A=2xr+\pi r^2$

The perimeter is $2x+2\pi r=400$
so $x+\pi r=200$
so $x=200-\pi r$