Question about deriving volume of a sphere

https://imgur.com/a/ScMPl

Hello, I have been wrestling for this one for a while. I am trying to derive the volume of a sphere. I am able to derive the correct volume (4πr^3/3) using various other methods, however i tried doing it using sines and cosines and I always get 1/2 the actual result. I have included my work. I hope it is clear to follow. If anyone has any questions to clarify let me know.