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Searching for ## Volume and Surface Area of Cones, Cylinders, and Spheres

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Algebra Foundations

Students will derive the formula for the volume of a cone from the formula for the volume of a pyramid.

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After completing this tutorial, you will be able to complete the following:

- Derive the formula for the volume of a cone from the formula for the volume of a pyramid.
- Explain the changes in the volume of a cone when its dimensions change.
- Calculate the volume of a cone.

In order for students to successfully complete this Activity Object, they should be familiar with the following shapes and their attributes, and volume formula.

- cylinder
- volume of a cylinder =
- triangular pyramid - A polyhedron with a three-sided base and four triangular sides meeting at a point (the apex).
- volume of a pyramid = , where a = area of the base of the pyramid.
- volume - the amount of space occupied by a three-dimensional object, expressed in cubic units

The students should also feel comfortable performing operations on rational numbers (a number which can be expressed as a ratio of two integers) and using the Pythagorean Theorem .

Approximate Time | 20 Minutes |

Pre-requisite Concepts | attributes of cylinders and pyramids, operations on rational numbers, Pythagorean Theorem, volume formulas of a cylinder and pyramid |

Course | Algebra Foundations |

Type of Tutorial | Visual Proof |

Key Vocabulary | 3D, cone, container |