Finding volume of solid using shell method.

Rotating the region bounded by $y={x}^{3},y=0,x=2$ around the line $y=8$.

I just want to double check if my initial formula is on the right track.

${V}_{y}={\int}_{0}^{8}(8-y)({y}^{\frac{1}{3}})dy$

Rotating the region bounded by $y={x}^{3},y=0,x=2$ around the line $y=8$.

I just want to double check if my initial formula is on the right track.

${V}_{y}={\int}_{0}^{8}(8-y)({y}^{\frac{1}{3}})dy$