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

## Formula for the Volume of a Cone                   Searching for

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

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Explore the full path to learning Volume and Surface Area of Cones, Cylinders, and Spheres ### Lesson Focus

#### Formula for the Volume of a Cone

Algebra Foundations

Students will derive the formula for the volume of a cone 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 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