Cross Sections Prisms and Pyramids

A square pyramid is intersected by a plane passing through the vertex and perpendicular to the base. Which two-dimensional shape describes this cross section?

• square

• triangle

• pentagon

• rectangle

In the diagram below, a plane intersects a square pyramid parallel to its base. Which two-dimensional shape describes this cross section?

• circle

• square

• triangle

• pentagon

Which figure(s) below can have a triangle as a two-dimensional cross section?

• I, only

• IV, only

• I, II, and IV, only

• I, III, and IV, only

The cross section of a regular pyramid contains the altitude of the pyramid. The shape of this cross section is a

• circle

• square

• triangle

• rectangle

Based on Cavalieri's Principle, will the two prisms have the same volume?

• No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

• Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.

Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.

• True

• False - the cross sectional areas are not relevant

• False - only the slant height is relevant

• False - even if they have the same cross sectional areas and heights, they cannot have the same volume.

What two-dimensional figure will be created by a vertical cross section?

• triangle

• rectangle

• hexagon

• octagon

Two different cross sections are taken parallel to the base of a three-dimensional figure. The two cross sections are the same shape, but are not congruent. Which could be the three-dimensional figure? Select three options.

• cone

• cylinder

• triangular prism

• triangular pyramid

• square pyramid

A three-dimensional shape is sliced. The results from slicing are a triangle, a rectangle, and a trapezoid. What was the original 3D shape?

• Triangular Prism

• Triangular Pyramid

• Rectangular Pyramid

• Rectangular Prism

What is a cross section of a three-dimensional object?

• The intersection of two lines on a graph.

• A two-dimensional shape created by slicing the object in various ways.

• The multiplication symbol.

• Any angle on the object that has a measure of 90 degrees.