Solids of Known Cross sections(volume)

The base of a solid is bounded by y=x^3, y=0, and x=1. Find the volume of the solid for each of the following cross sections perpendicular to the y-axis.

a)semicircles

b)Squares

-MY STEPS

a)$\displaystyle A =\frac{\pi r^2}{2}$

$\displaystyle r = (\sqrt[3]{y/2})$

$\displaystyle V = \pi /4 \int_{0}^{1} (\sqrt[3]{y})^2$

V=.4712319

(Did I do this right?)

b)$\displaystyle A=D^2$

$\displaystyle D=\sqrt[3]{y}$

$\displaystyle V=\int_{0}^{1}(\sqrt[3]{y})^2$

V=.600000

(did I do this right?)

I don't think I did these right. Can someone help me out. Thanks.