kill(all)$

load(ntrig)$ load(atrig1)$

van=facebook.com/LearningCalculus$

      See Derivation at https://planetcalc.com/1442/

theta(x):=2*acos((R-x*tan(%pi/2-%pi/3))/R);

assume(L>0,R>0)$

V(L,R):=R^2/2*   integrate(theta(x)-sin(theta(x)),x,0,L)
       =R^2/2*''(integrate(theta(x)-sin(theta(x)),x,0,L))$

factor(%);

rhs(float(V(4,3)));

assume(x>0,y>0)$

rhs(V(x,y));

float(40/3);