Calculating Area and Perimeter of Geometric Figures with pi^2 and (pi^2-1)

[arivero]

Is there any geometric figure whose calculation (area, perimeter, ...) involves the terms pi^2 or (pi^2-1) ?

 

[HallsofIvy]

I thought it was pretty well known that the area of a circle of radius r is
\pi r^2?

 

[arildno]

Is there any geometric figure whose calculation (area, perimeter, ...) involves the terms pi^2 or (pi^2-1) ?

Sure, check up the torus..
The surface area of a torus with big radius R and small radius r has surface area:
A=4\pi^{2}Rr (r<R)

 

[robphy]

Here are some higher-dimensional expressions
http://thinkzone.wlonk.com/MathFun/Dimens.htm