Let the region R be the area enclosed by the function
�
(
�
)
=
�
3
f(x)=x
3
and
�
(
�
)
=
4
�
.
g(x)=4x. If the region R is the base of a solid such that each cross section perpendicular to the
�
x-axis is a rectangle whose height is half the length of its base in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth.