Question

a cylinder is shown.
how can the cylinder be cut so that the cross section is the largest rectangle?
cut perpendicular to the base dropdown the center.
dropdown options: and through, but not through

Explanation:

Step1: Recall Cylinder Cross - Section

A cylinder has a circular base. When we cut a cylinder perpendicular to the base, the cross - section related to the circular part: the diameter of the circular base is the longest chord in the circle.

Step2: Determine the Cut for Largest Rectangle

To get the largest rectangle as a cross - section when cutting perpendicular to the base, the cut must pass through the center of the circular base (and also the center of the top circular face). Because the length of the rectangle's side related to the circle will be the diameter (the longest possible chord) when we cut through the center. If we don't cut through the center, the length of that side will be less than the diameter, so the area of the rectangle (which is length×height, where height is the height of the cylinder) will be smaller. So we need to cut perpendicular to the base and through the center.

Answer:

and through