Question

which solids have the same types of vertical cross sections through the base?a rectangular prism and a cylinder
a rectangular prism and a cone
a cylinder and a cone
a cylinder and a pyramid

Explanation:

To determine which solids have the same vertical cross - sections through the base, we analyze each option:

1. Option 1: Rectangular prism and cylinder

• For a rectangular prism, when we take a vertical cross - section through the base (assuming the base is a rectangle), the cross - section is a rectangle.
• For a cylinder, when we take a vertical cross - section through the base (the base is a circle), the cross - section is a rectangle (if we consider the cross - section parallel to the axis of the cylinder).

1. Option 2: Rectangular prism and cone

• A vertical cross - section through the base of a rectangular prism is a rectangle.
• A vertical cross - section through the base of a cone (the base is a circle) is a triangle (when the cross - section passes through the apex of the cone). So their cross - sections are different.

1. Option 3: Cylinder and cone

• A vertical cross - section of a cylinder through the base is a rectangle.
• A vertical cross - section of a cone through the base is a triangle (when passing through the apex) or a trapezoid (when not passing through the apex), which is different from the rectangle of the cylinder.

1. Option 4: Cylinder and pyramid

• A vertical cross - section of a cylinder through the base is a rectangle.
• A vertical cross - section of a pyramid (e.g., a square pyramid with a square base) through the base is a triangle (if it's a triangular - faced pyramid) or a trapezoid (if it's a non - regular pyramid), which is different from the rectangle of the cylinder.

Answer:

a rectangular prism and a cylinder