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ZingPath: Volume and Surface Area of Cones, Cylinders, and Spheres

Formula for the Volume of a Sphere                   Searching for

Volume and Surface Area of Cones, Cylinders, and Spheres

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Lesson Focus

Formula for the Volume of a Sphere

Algebra Foundations

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

Now You Know

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.

Everything You'll Have Covered

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

Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts attributes of pyramids, formula for the volume of a pyramid, regular triangular pyramid, surface area of a sphere, vertices (base and top) Course Algebra Foundations Type of Tutorial Visual Proof Key Vocabulary volume, sphere, pyramid