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Math Foundations

Observe the changes that occur in the volume of a quadrilateral pyramid when the area of the base, height, and incline change.

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

- After completing this Activity Object, learners will be able to:
- Recognize that the volume of a quadrilateral pyramid is equal to one-third of the product of its height and the area of the base.
- Recognize that the volume of a quadrilateral pyramid is proportional to both its height and area of the base.
- Recognize that the volume of a quadrilateral pyramid does not change when its incline changes.

A quadrilateral pyramid is a three-dimensional geometric figure.

A quadrilateral pyramid has a quadrilateral (four-sided) base with four triangular sides meeting at a point (the apex). If the base is a square, it is called a square pyramid.

The volume of a pyramid can be found by using the formula

The volume of a quadrilateral pyramid is equal to one-third of the product of its height (h) and the area of its base (B). To find the volume of a quadrilateral pyramid, first we need to calculate the area of its base (B).

The volume of a pyramid is proportional to both its height and area of its base.

This Activity Object will focus on the changes in a quadrilateral pyramid's volume when other variables are altered. For instance, students will be able to change the area of the base, the height, and the incline of the quadrilateral pyramid, and then observe the results from these changes.

- When only the height is changed
- The volume of a quadrilateral pyramid is proportional to its height. What this means is that if the height is increased the volume increases, and if the height decreases the volume decreases.
- When only the area of the base is changed
- The volume of a pyramid is proportional to the area of its base. What this means is that if the area of its base is increased the volume increases, and if the area of its base decreases the volume decreases.
- When the height AND area of the base are both changed
- Because the volume of a pyramid is proportional to its height and the area of its base, the volume will change when the height and area of the base of the pyramid change.
- When the incline is changed
- The volume of a pyramid does not change when its incline changes. This is because when the incline changes, the area of the base and height do not change.

- The following key vocabulary terms will be used throughout this Activity Object:
- area of the base -the area of the quadrilateral base of the pyramid
- height - the perpendicular distance to the base
- incline - the slant (to the right or left) or slope of a three-dimensional shape
- quadrilateral pyramid - a polyhedron with a four-sided base and four triangular sides meeting at a point (the apex)
- volume of a pyramid
- (V: Volume, B: Area of the base and h: height)

Approximate Time | 15 Minutes |

Pre-requisite Concepts | Area of the base, height, incline, quadrilateral pyramid, volume of pyramid |

Course | Math Foundations |

Type of Tutorial | Dynamic Modeling |

Key Vocabulary | area of the base, base, height |