Final answer:
The volume of the described solid (cylinder) is given by V=πr2h, where r is the radius of the circular base and h is the height.
Step-by-step explanation:
The student is asking to find the volume of a solid with a circular base and square cross sections perpendicular to the base's axis.
To do this, we must consider the formula for the volume of a cylinder, which is the cross-sectional area times the height (V = Ah). For a solid with square cross sections, the area of each square is equal to the side length squared (a²), where the side length is the diameter of the base circle.
If the diameter of the circle is d, then the area of each square cross section would be d². You would integrate this area along the height of the solid to find the total volume.
Since the base is a circle, it is helpful to note that the circle's diameter will equal the side length of the square, which is a = 2r where r is the radius of the circle.
Consequently, the area for the square cross-section would be (2r)² = 4r². You would then integrate this area from the bottom to the top of the solid to find the volume.
Your correct question is: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 4 with square cross sections taken perpendicular to the x-axis. O 43.786 O 51.345 42.667 39.456