Find the volume of the solid whose base is bounded by the circle x^2+y^2=4 with Equilateral triangle cross sections taken perpendicular to the x-axis.
area of an equilateral triangle of side length "$\displaystyle s$" is $\displaystyle A = \frac{\sqrt{3}}{4} s^2$
for your problem, the side of an equilateral cross-section is $\displaystyle s = 2y$.
equation for the volume of the described solid is
$\displaystyle V = \int_{-2}^{2} A(x) \, dx$
get the cross-sectional area as a function of x and integrate.