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Geometric Formulas


Videos and lessons to help High School students learn how to give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Common Core: HSG-GMD.A.1 and HSG-GMD.A.2

Related Topics:
Common Core (Geometry)

Common Core for Mathematics

Circumference of a circle, 2πr, How to get the Formula.

Area of a circle, how to get the formula.

Surface Area of a Cylindrical Solid
Explanation of the origins of the formula for the surface area of a cylinder.

Volume of a Pyramid, Deriving the Formula
Animated proof that volume of a pyramid is equal to Bh/3.
Sum of integers squared, formula explanation.


Cavalieri's Principle
If two solids lying between parallel planes have equal heights and all cross sections at equal distance from their bases have equal areas, then the solids have equal volumes.

Formula for the Volume of a Cone
This video explain why the volume of a cone is 1/3 the volume of the cylinder that surrounds it. It uses Cavalieri's Principle.

Volume of a Sphere, How to get the formula animation
(4/3)πr3 gives you the volume of a sphere, but where does the formula come from? Here is a simple explanation using geometry and algebra.

Surface Area of a Sphere, deriving the formula
Proof that Surface Area of a Sphere is equal to 4πr2 using geometry and algebra.


Formula for the Volume of a Sphere
This video shows how Archimede's deduced found the volume of a sphere. To do so he had to use a formula for the volume of a cone.

Formula for Surface Area of a Sphere
This video shows how Archimede's deduced that the surface area of a sphere is 4πr2 after having figured a formula for its volume.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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