Final answer:
The volume of the solid can be computed by finding the area of the base and the height. The base is a triangle formed by the lines x+y=23, x=0, and y=0. The cross sections perpendicular to the y-axis are semicircles.
Step-by-step explanation:
The base of the solid is a triangle formed by the lines x+y=23, x=0, and y=0. To compute the volume of the solid, we need to find the area of the base and the height of the solid. The cross sections perpendicular to the y-axis are semicircles, so the area of each cross section is half the area of a circle with radius equal to the distance from the y-axis to the triangle.
The distance from the y-axis to the triangle is the x-coordinate of the point where the triangle intersects the line x+y=23. Solving the system of equations, we find that this point is (11, 12). So, the radius of each semicircle is 11 units and the height of the solid is 12 units.
Now, we can compute the volume using the formula V=Ah, where A is the area of the base and h is the height. The area of a circle is given by A=πr^2, so the area of each semicircle is A=π(11^2)/2. Plugging in the values, we get V=π(11^2)/2(12), which simplifies to V=121π.