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. cone

D. triangular pyramid

E. square pyramid

(Photo for proof at the bottom.)

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.

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

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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