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# ZingPath: Volume

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## Volume

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### Lesson Focus

#### Observing Changes in the Volume of Square Prisms

Geometry

The changes that occur in the volume of a square prism by changing the variables of the square prisms’ area of the base, height, and incline of a right square prism is observed.

### Now You Know

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 square prism is equal to the product of its height and area of the base.
• Explain that the volume of a square prism is proportional to both its height and area of the base.
• Explain that the volume of a square prism does not change when its incline changes.

### Everything You'll Have Covered

A right square prism is a three-dimensional geometric figure.

A right square prism is a polyhedron consisting of two parallel, congruent faces called bases that are joined by faces that are parallelograms. These bases are perpendicular to the lateral faces of the prism, therefore the prism is considered to be a right prism. A right square prism which has square lateral faces is called a cube.

The volume of a right square prism can be found by using the formula

The volume of a square prism is equal to the product of its height (h) and the area of its base (B).

The volume of a right square prism is proportional to both its height and area of its base.

This Activity Object will focus on the changes in a right square prism'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 square prism, and then observe the results from these changes.

• When only the height is changed
• The volume of a right square prism 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 right square prism 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 right square prism 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 right square prism 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 base of the prism
• height - the perpendicular distance to the base
• incline - the slant (to the right or left) or slope of a three-dimensional shape
• right square prism - a polyhedron consisting of two parallel, congruent and square bases that are perpendicular to the lateral faces of the prism
• volume of a square prism

### Tutorial Details

 Approximate Time 15 Minutes Pre-requisite Concepts Students should know the definition of a right square prism, incline, and height, and be able to calculate the volume of a prism and the area of the base of a prism. Course Geometry Type of Tutorial Skills Application Key Vocabulary area of the base, height, prism