Make a Conjecture

What cross sections might you see when a plane intersects a cone that you would not see when a plane intersects a pyramid or a prism?

Critical Thinking

The two figures on the left below show that you can form a cross section of a cube that is a pentagon. Think of a plane cutting the cube at an angle in such a way as to slice through five of the cube’s six faces. Draw dotted lines on the third cube to show how to form a cross section that is a hexagon.

Analyze Relationships

A sphere has a radius of 12 inches. A horizontal plane passes through the center of the sphere.

a. Describe the cross section formed by the plane and the sphere

b. Describe the cross sections formed as the plane intersects the interior of the sphere but moves away from the center.

Communicate Mathematical Ideas

A right rectangular prism is intersected by a horizontal plane and a vertical plane. The cross section formed by the horizontal plane and the prism is a rectangle with dimensions 8 in. and 12 in. The cross section formed by the vertical plane and the prism is a rectangle with dimensions 5 in. and 8 in. Describe the faces of the prism, including their dimensions. Then find its volume.

Represent Real-World Problems

Describe a real-world situation that could be represented by planes slicing a three-dimensional figure to form cross sections.