Question

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

Answer 1

A. cone

D. triangular pyramid

E. square pyramid

(Look at the photo at the bottom.)

Explanation:

First, know what a cross section is. A cross section is the exposed shape or surface when a straight cut is made through a 3D figure. For example, if I make a cross section, or cut, through a sphere, the cross section will be a circle. The newly exposed surface is in the shape of a circle.

We want to know which 3D figures can make 2 different cross sections, parallel to the base, that are congruent. Congruent means same shape but different size. Parallel to the base means the cut is completely horizontal.

• A cone is one, because no matter where you horizontally cut this, the cross section will always be a circle, but different sizes.
• A triangular pyramid is another, because no matter where you horizontally cut this, the cross section will always be a triangle, but different sizes.
• A square pyramid is another, because no matter where you horizontally cut this, the cross section will always be a square, but different sizes.

Here's a photo of Edge incase you're doubtful.