In this next section, you are expected to calculate the volume of cones and pyramids.
Here is a quick reference for calculating the volume of cones and pyramids.
Notice that both 3D shapes come to a point! Notice that both are divided by 3, is it a coincidence? Nope.
To calculate the volume of the cone, first calculate the area of the circle by multiplying the radius times itself then by pi. Next, multiply the area number by the height of the cone. Lastly, divide your answer by 3. That’s it!
To calculate the volume of a pyramid, find the area of the base (square) by multiplying the length times itself. Multiply this answer by the height. Now divide by 3. Done!
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Check for assignments (click on classes to see this) Current assignments due: 1) Online Learning Connection Check In 2) Readiness Quiz 3) Interactive Student Edition Lesson 11-2 4) Lesson 11-2 Quiz 5) Three Acts
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.
