Final answer:
The volume of the solid in question, with a circular base and isosceles right triangular cross-sections, can be found by integrating the area of the triangles across the diameter of the circular base.
Step-by-step explanation:
The student is asking for help in finding the volume of a solid with a circular base where the equation of the circle is x^2 + y^2 = 121. This indicates that the radius of the base circle is 11. Given that cross-sections perpendicular to the x-axis are isosceles right triangles with legs in the xy-plane, the area of each triangle will be A = 1/2 × base × height. Since the triangles are isosceles right triangles, the base and height are equal, which means the area can also be expressed as A = 1/2 × s^2, where s is the length of a leg.
To find the volume, we use the formula V = A × h, where A is the cross-sectional area and h is the height. In this case, the 'height' is the diameter of the base circle since the cross sections are perpendicular to the x-axis. Integrating the area of these triangles from -11 to 11 (the limits being the diameter of the base circle), we can calculate the volume of the solid.