### Learning Targets:

I can describe that as soon as a 3 dimensional number is sliced it create a face that is two dimensional.I can snapshot different overcome sections that prisms and pyramids.

You are watching: Cross sections of a square pyramid

Describe each shape as precisely as you can. Click on the applet and drag the computer mouse to display the object transforming in 3D.

Here space a rectangular prism and also a pyramid through the very same base and also same height. Drag the big red suggest up and down to relocate the airplane through the solids.

If we slice each hard parallel come its basic halfway up, what shape cross sections would certainly we get? What is the same about the overcome sections? What is different?

If we slice each heavy parallel to its base near the top, what shape cross sections would certainly we get? What is the same around the overcome sections? What is different?

### Are you prepared for more?

Describe the overcome sections that would an outcome from slicing every solid perpendicular to its base.

Your teacher will offer you a set of cards. Kind the photos into groups that make feeling to you. Be prepared to explain your reasoning.

Use the applet to attract each overcome section and also describe the in words.

Here is one applet v a rectangular prism, 4 devices by 2 devices by 3 units.

A aircraft cuts the prism parallel come the bottom and top faces.The plane moves up and also cuts the prism at a various height.A vertical plane cuts the prism diagonally.
A square pyramid has a base that is 4 devices by 4 units. Its height is likewise 4 units.A airplane cuts the pyramid parallel to the base.A vertical plane cuts the prism.
A cube has actually an edge of length 4.A aircraft cuts off the edge of the cube.The airplane moves farther native the corner and also makes a cut through the center of the cube.

## Lesson 11 Summary

When we slice a three-dimensional object, us expose brand-new faces that room two dimensional. The two-dimensional challenge is a cross section. Numerous different overcome sections are feasible when slicing the same three-dimensional object.

Here space two peppers. One is sliced horizontally, and also the other is sliced vertically, producing different overcome sections.

The imprints the the slices represent the two-dimensional faces created by every slice.

It takes practice imagining what the cross section of a three-dimensional object will be for various slices. It helps to experiment and see for yourself what happens!

## Glossary Terms

cross section

A cross ar is the new face you see as soon as you slice v a three-dimensional figure.

For example, if you part a rectangle-shaped pyramid parallel to the base, you get a smaller rectangle together the overcome section.

## Lesson 11 practice Problems

A cube is reduced into 2 pieces by a single slice that passes through point out A , B , and also C . What shape is the overcome section?

Describe just how to slice the three-dimensional figure to result in every cross section.

Here room two three-dimensional figures.

Each row consists of the degree measures of two supplementary angles. Complete the table.

measure ofan anglemeasure ofits supplement
80^\circ
25^\circ
119^\circ
x

Two months ago, the price, in dollars, that a cell phone was c .

Last month, the price the the phone boosted by 10%. Write an expression for the price that the phone critical month.This month, the price of the phone diminished by 10%. Create an expression because that the price the the phone this month.Is the price of the call this month the exact same as that was two months ago? define your reasoning.

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