Question: using maple to find the dimensions of a right cylinder who's maximum volume can be inscribed in a sphere of 10 cm

I under stand how to do the calculus that's easy enough, but Maple is stil giving me a hard time.  The math par t is let the radius of the cylinder be r cms. 0<r<10 Then the height is 2 * Sqrt 100-r^2, the volume is V(r)=2PIr^2* sqrt 100-r^2 cm^3

Differentiante V(r) with respect to r we get V' (r) =2PIr^2(1/(2*sqrt(100-r^2)))(-2r) + (2PIsqrt(100-r^2))(2r)

V'(r)=(-2PIr^3 +4PIr(100-r^2))/sqrt (100-r^2)      V'(r)=2PIr(200-3r^2)/sqrt 100r^2         to find the critical point find the value of r when V(r) =0     2PI(200-3r^2)/sqrt 100-r^2 =0   2PIr(200-3r^2) = 0   r(200-3r^2)=0 

r=0 or 200-3r^2 =0     r=0 or r^2=200/3 r=sqrt(200/3) =10sqrt(2/3)   r is not in the interval so ignore it.  The critical point for 0<r<10 occurs at r = 10sqrt(2/3)       Since V'(r) >0 for 0<r<10sqroot(2/3) and V'(r) <0<10sqrt(2/3)<10

The dimensions are r=10sqrt(2/3) =8.16 cm and h=20/sqrt3 = 11.55 cm the volume is 4000PI/3*sqrt3=2418.4 cm^3

So how do I translate this into maple? Any help is greatly appreciated.