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Geometry

The formula for the volume of a sphere is derived 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 sphere from the formula for the volume of a pyramid.

In this Activity Object, students will begin by locating regular triangular pyramids within a sphere. The height of the pyramids and the radius of the sphere are then compared, along with the empty space left between the pyramids and the sphere's surface. The student is given the opportunity to observe what happens when the numbers of pyramids are increased and decreased. They will observe that when the number of pyramids is increased, the Sum of the Area of the Bases of the Pyramids approaches the Surface Area of the Sphere. Based on these observations, and the Volume of a Pyramid, the student is then asked to derive the formula for the Volume of a Sphere .

The following key vocabulary terms will be used throughout this Activity Object:

- volume - the amount of space occupied by a three-dimensional object expressed in cubic units
- sphere - a three-dimensional surface, all points of which are equidistant from a fixed point

Approximate Time | 20 Minutes |

Pre-requisite Concepts | Students should know the properties of a pyramid, the formula for the volume of a pyramid, the surface area of a sphere, and the meaning of vertices (base and top). |

Course | Geometry |

Type of Tutorial | Visual Proof |

Key Vocabulary | volume, sphere, pyramid |