Second Semester Geometry

Survival Guide

Chapter 10: Volume

Big Idea1. A prism is a solid bounded by 2 congruent faces called bases that lie in parallel planes. The other faces are parallelograms formed by connecting the corresponding vertices of the bases.2. The height of a prism is the perpendicular distance between its bases.3. Right prisms have lateral edges that are perpendicular to both bases; oblique prisms have lateral edges that are perpendicular to the bases.

Cross Sections of Prisms

  • A cross section is a view into the inside of something made by cutting through it.



  • Cross sections make a different shape depending on where the cut is made.




Examples of Cross Sections

Volume of Prisms

Equations for Prisms

Prism/Cylinder=Base x Height                                                                          Pyramid/Cone=Base x Height x 1/3                                                                                   **Measured in Units Cubed

Area of the Base

Prism=Length x Width; Cylinder=Pi radius squared; Pyramid=whatever the shape is determines the equation; Cone=same as Cylinder; -agonal bases=see picture
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Sphere Formula

Sphere=4/3 x Pi x radius cubed
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Composite Shapes

You split the shapes up, find the volume of each, and add/subtract the numbers to get the total volume.
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Tips!

  • Use a calculator-it makes it much easier to solve
  • Write out all parts of the problem so you don't miss a simple step

Things I Struggled With

  • Visualizing the shapes in my head
  • That's it it was pretty simple!