## Volume of Cylinders and Triangular Prisms

#### Aligned To Common Core Standard:

**Geometric Measurement** - HSG-GMD.A.3

How to find the Volume of Cylinders and Triangular Prisms?
We all are familiar with three-dimensional shapes. Three-dimensional shapes are defined by three characteristic properties, i.e., height, length, and width. We all observe these shapes in our daily life. From our ice-cream to basketballs, three-dimensional shapes are found everywhere around us.
You must have enjoyed a soft drink can. But have you ever built a camping tent?
**Triangular Prisms** - Camping tents have a triangular prism shape. Mathematically, a triangular prism is a polyhedron (a solid figure having many plane faces) combination of triangles and rectangles. A triangular prism has three sides with three edges and two triangular bases. Its sides are in rectangular, and the edges of triangular prism connect the corresponding sides. It bases have equilateral triangles with their edges being parallel to each other.
**Volume Of The Triangular Prisms** - The formula finds the volume of the triangular prism, V= 1/2 x b x h x l
Where, b is the base length, h is the height of the triangle, l is the length between the triangular bases.
**Cylinders** - Our food cans, soft drink cans have a cylindrical shape. A cylinder is a 3d shape with two identical flat sides and one curved side. Cylinders have the same cross-section throughout.
**Volume** - The formula can find the volume of the cylinder,
V= Π x r^{2} x h Where, Π (constant) is taken as 3.14, r is the radius of the circular end of the cylinder, h is the height of the cylinder.

### Printable Worksheets And Lessons

- Triangular Prism Step-by-step Lesson - Yes, a cylinder, but also a triangular prism to work with.
- Guided Lesson - These are not as tough as previous work under this standard.
- Guided Lesson Explanation - After working with abstract geometry all day, these are a pleasure to explain.
- Practice Worksheet - The shapes are colored and very large to help.
- Matching Worksheet - Find the volume and the cross-sectional size with this one.

#### Homework Sheets

These are equations that you will want your students to have experience with.

- Homework 1 - Volume of a triangular prism: Volume= 1/2 × base× height × length. remember to place the proper units.
- Homework 2 - Volume of a cylinder: Volume = Π r
^{2}h. These are some pretty plump cylinders that will hold a lot of something. - Homework 3 - Use that formula to put everything together. This serves as a good practice set.

#### Practice Worksheets

For some odd reason the cylinder really gives students trouble.

- Practice 1 - What is the volume of this cylinder? Given the measures and use proper units.
- Practice 2 - Use these numbers in the volume formula to solve a series of problems for yourself.
- Practice 3 - A different approach to this technique can be used.

#### Math Skill Quizzes

I used color in the objects to add a degree of depth and perspective of the objects.

### Where Do We Regularly Use These Measures?

You would be surprised by how often corporations have people working on this very skill set. Think about all the products you have in your home that are cylinder shaped. Do you think Pepsi or Coca Cola carries about this measure? Of course, they do when they sell North of twenty-five billion dollars of their product in cylindrical cans. Both of these companies have tested selling a can that held less volume than their traditional twelve ounce can. The point being to make people pay the same amount for less. Yeah, that did not go over too well with customers. Besides soda cans, this applies to all types of products coffee, ice cream, candles, and even cans of tennis balls. You will find that triangular prism measure of volume common when determining the capacity of an upstairs attic. You will also find this a critical measure of most camping tents which indicates how many people can use it for shelter, primarily sleeping.