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

Formula for the Volume of a Cone

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Volume and Surface Area of Cones, Cylinders, and Spheres

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Lesson Focus

Formula for the Volume of a Cone

Algebra Foundations

Learning Made Easy

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

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Now You Know

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.

Everything You'll Have Covered

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 .

Tutorial Details

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