cylinder volume = base x height = (pi * r²)* (2r) = 2 pi r³

and

cone volume = 1/3 x base x height = 1/3 x [pi * (2r)²] * (2r) = 8/3 pi r³

    so Archimedes reasoned that

1 x (cone volume + sphere volume) = 1/2 x (4 cylinder volumes)

sphere volume = 2 cylinder volumes - cone volume

sphere volume = 2 x (2 pi r³) - 8/3 pi r³

sphere volume = 4/3 pi r³

back