Demonstration of the Volume of a Cone compared to the volume of an equal sized cylinder using water.
In this demonstration, you will see how the volume of a cone is 1/3 the volume of a cylinder that has an equal radius and height.
The volume of a cylinder is equal to πr^2 x height
The volume of a cone equals 1/3 πr^2 x height
Therefore, it should take three cones of water to fill up an equal sized cylinder.
This video gives direction for finding the perimeter of a rectangle when only one side is given.
The diagonal of a rectangle creates a right triangle that can be used to find the missing side.
Common Core Standard G-GPE.7
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How to set up trig ratios with a right triangle.
The video demonstrates how to set up a trig function in order to find missing length and angles of a right triangle.
Follow these steps to set up trig functions properly.
The first step is to find the reference angle.
Next, label the opposite,adjacent,hypotenuse sides of the right triangle.
Finally, decide which trig function to use and then set it up.
The trig functions used in this video are:
Sine=Opposite over hypotenuse
Cosine=Adjacent over hypotenuse
Tangent= Opposite over adjacent
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0:06 Introduction to adding and subtracting functions
0:03 Problem 1,add g(x) +j(x)
1:21 Solution to problem 1 (Adding functions)
1:36 Problem 2 Subtract functions j(x) -g(x)
3:07 Solution to problem 2
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How to simplify complex fractions
Complex fractions have a fraction on top of a fraction
Video Guide
0:46 Simplify 5+7/11 / 5/12
0:51 Simplify the numerator of the complex fraction =12/11
0:58 Don't simplify the denominator but move the fraction over so the complex fraction becomes 12/11 divided by 5/12
1:35 Change the problem from division to multiplication by Keeping the first fraction the same, changing the sign,flipping the last fraction
2:22 Answer to first simplifying complex fractions problem
2:39 Problem 2 Simplify the complex fraction 3/4 + 2/3 /1/2
2:54 Simplify the numerator of the complex fraction by finding a common denominator
3:51 After simplifying the numerator you get 17/12 divided by1/2
4:06 Apply Keep in Change it Flip it
4:42 Answer to problem 2
5:05 Simplify the complex fraction that contains variables
1/2 + 1/x /x^2 + 2x
5:12 Simplify the numerator by finding a common denominator
6:23 Use the keep it Change it Flip it rules to turn the problem from division to multiplication
7:30 Final answer "Simplify a complex fraction with variables"
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