Quiz

I messed up, you figure it out...

ok

0.5 πρgR^3 (H/R - (1/3)sin(3arcsin(H/R))) = ...
Triple angle sine sin(3x) = 3 sin x - 4 sin^3 x
... = 0.5 πρgR^3 * 4 (H/R)^3 = 2 πρgH^3 ----------------- (3)

There seems to be an error here.
Here is the expression in the last parentheses
H/R - (1/3)sin(3arcsin(H/R)) = H/R - (1/3)*(3(H/R) - 4(H/R)^3) = H/R - H/R + (4/3)(H/R)^3 = (4/3)(H/R)^3

Then it will not be

2 πρgH^3