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, Cavalieris principle,
and informal limit arguments*.

Give an informal argument using Cavalieris 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

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)πr

Surface Area of a Sphere, deriving the formula

Proof that Surface Area of a Sphere is equal to 4πr

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 4πr

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