Cross Sections

Warm Up

An intersection is a point or set of points common to two geometric figures. A cross section is the intersection of a three-dimensional figure and a plane. A three-dimensional figure can have many different cross sections. The shape of a cross section depends on the angle and the placement of the slice.

A cone is sitting on top of a cylinder A cone is sitting on top of a cylinder. The two figures have equal radii. Describe the cross section that slices through the combined figures. Draw a picture to illustrate your answer.

Describing Cross Sections Visualize the shape of an intersection created by a flat plane cutting into a three dimensional object. The angle of the slice changes the size and shape of a cross section. A plane slicing a solid figure parallel to the figure’s base will create a cross section the same shape as the base of the figure.

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?

A sphere has a radius of 12 inches 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.

Exit Ticket Describe each cross section. Is it possible for a cross section of a cylinder to have a triangular shape?