Question

a cylinder is shown.
how can the cylinder be cut so that the cross section is the largest rectangle?
cut ▼ to the base ▼ the center.

Explanation:

Step1: Analyze Cylinder Structure

A cylinder has a circular base. The diameter is the longest chord in a circle. For a rectangular cross - section, we need to consider the orientation of the cut.

Step2: Determine Cut Orientation

To get the largest rectangle, we should cut the cylinder perpendicular to the base (so that the height of the cylinder is one side of the rectangle) and pass through the center (so that the length of the rectangle is the diameter of the circular base, which is the maximum possible length for the horizontal side of the rectangle). If we cut parallel to the base, the cross - section would be a circle or a smaller rectangle (if not passing through the center), and non - perpendicular cuts would result in non - rectangular or smaller rectangular cross - sections. So the first blank should be "perpendicular" and the second blank should be "through".

Answer:

First blank: perpendicular; Second blank: through