Second Semester Geometry
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
You could get a cross section of a square and rectangle (above) and a triangle.
You could get a cross section of a rectangle, circle, or oval.
You could get a cross section of a triangle or a square.
Volume of Prisms
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
Sphere=4/3 x Pi x radius cubed
You split the shapes up, find the volume of each, and add/subtract the numbers to get the total volume.
- 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!