Envision 11-2 Assignment

In this lesson you will be expected to calculate the volume of a prism and a cylinder.

Here are the formulas for quick reference:

Let’s break this down a little bit.

First, volume is the measure of how much space there is inside of something, in this case a prism type shape. You can think of a prism as a 2D shape that is stretched to make a 3D version of itself. Look at the triangular prism as an example.

To calculate volume, we multiply all 3 measurements, height or depth, width, and length. Sometimes, a shape doesn’t have an easy width and length like a circle, so we can also think of the calculation of volume as the area of the 2D shape times the height of the 3D prism. Since volume is found by multiplying 3 dimensions together, the units are to the third power or what we called cubed.

To recap, the volume of a rectangular prism is its length times width times height.

The volume of a triangular prism is one-half times its base (which is really its length) times its height.

The volume of a cylinder is pi times the radius of the circle squared (times itself) times the height. Remember pi is about 3.14 if you don’t have a pi button on your calculator. Also, if you are given the diameter of the circle, you need to divide that number by 2 (cut it in half) in order to have the radius 😉

So, where did some shape’s area formulas come from? That’s a great question. I’m so glad you asked. Let’s look at the triangle. To calculate the area of a 2D triangle, it is 1/2 times the base length times the height. Well, when we are calculating area, length times height should sound familiar. But, where does the 1/2 come from? Think about this. If we had a rectangle, the area would be just the length times the height. How does a triangle relate to a rectangle? It’s half!

So, to find the area of a triangle it’s 1/2 the area of what the rectangle would be.

Please complete the Do You Understand, Do You Know How sections and the lesson quiz by 11:59 on Wednesday, March 25.