Question

which three - dimensional solid can have a vertical cross section that is a circle with a radius of 7?

Explanation:

Step1: Analyze the first solid (cylinder)

A vertical cross - section of a cylinder (when the cross - section is parallel to the base) is a rectangle. But if the cross - section is perpendicular to the height (horizontal cross - section), it is a circle. However, the problem says vertical cross - section. If we consider a right - circular cylinder, a vertical cross - section (parallel to the axis of the cylinder) is a rectangle. But if we consider a circular cylinder (a cylinder with circular bases) and take a cross - section perpendicular to the height (horizontal cross - section), it is a circle. But let's check other solids.

Step2: Analyze the second solid (rectangular prism)

A rectangular prism (a box - like shape) has cross - sections. A vertical cross - section (parallel to the faces) will be a rectangle. It can never be a circle.

Step3: Analyze the third solid (cone)

A vertical cross - section (a cross - section passing through the axis) of a cone is a triangle. A non - vertical (horizontal) cross - section is a circle. But the problem asks for a vertical cross - section.

Step4: Analyze the fourth solid (cylinder - correct orientation)

If we consider a circular cylinder (a cylinder with circular bases) and we take a cross - section perpendicular to the height (a horizontal cross - section is a circle). But if we rotate the cylinder so that its height is in the horizontal direction. Then a vertical cross - section (perpendicular to the new height direction) will be a circle.

Answer:

The fourth three - dimensional solid (the cylinder oriented such that its height is horizontal)