Question

in each figure below, a plane passes through a geometric solid as shown. for each figure, choose the shape of the cross section formed. (a) (b) (c)

Explanation:

Step1: Analyze Figure (a)

The solid is a prism. When a plane cuts through it horizontally, the cross - section has two parallel sides (from the top and bottom of the prism part) and two non - parallel sides (from the slant of the upper part). This is the definition of a trapezoid.

Step2: Analyze Figure (b)

The solid is a cylinder. When a plane cuts through it vertically (not through the center in a special way), the cross - section is a rectangle. The two opposite sides are equal (from the height of the cylinder) and the other two opposite sides are equal (from the circular base's chord length).

Step3: Analyze Figure (c)

The solid is a cone. When a plane cuts through it horizontally (parallel to the base), the cross - section is a circle. Because all points on the cross - section are at an equal distance from the axis of the cone (similar to the property of a circle where all points on the circumference are at an equal distance from the center).

Answer:

(a) Trapezoid, (b) Rectangle, (c) Circle