The volume V of a solid between a and b is the integral of its cross-sectional area A(x) from a to b, or

The area A of an equilateral triangle is where is the length of a side. Since the trianglular cross-sections have their base in a circle with radius 1, the side of the triangular cross-section at any x is twice the distance from the x-axis to a semi-circle of radius 1, or . Therefore

Since your solid is enclosed in a circle with radius 1, you're going to integrate the area from -1 to 1, or which you should know how to do.