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

## Observing Changes in Volume of Cylinders                   Searching for

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

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### Lesson Focus

#### Observing Changes in Volume of Cylinders

Algebra Foundations

Observe the changes that occur in the volume of a cylinder when its height, radius, and incline change.

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

### Everything You'll Have Covered

A cylinder is a three-dimensional geometric figure.

A three-dimensional geometric figure that has two congruent and parallel circular bases connected to a curved surface. The volume of a cylinder can be found by using the formula The volume of a cylinder is equal to the product of its height (h) and the area of its base (B). To find the volume of a cylinder, first we need to calculate the area of its base (B). The area of the base (B) is equal to because the base is shaped like a circle. So, the volume of the cylinder is equal to the product of and the height (h). The volume of a cylinder is proportional to both height and the square of the radius of its base.

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

• When only the height is changed
• The volume of a cylinder 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 radius is changed
• The volume of a cylinder is proportional to the square of the radius of its base. What this means is that if the radius is increased the volume increases, and if the radius decreases, the volume decreases.
• When the height And radius are both changed
• Because the volume of a cylinder is proportional to its height and the square of the radius of its base, the volume will change when the height and radius of the cylinder change.
• When the incline is changed
• The volume of a cylinder does not change when its incline changes. This is because when the incline changes, the radius and height do not change.
• The following key vocabulary terms will be used throughout this Activity Object:
• area of the base -the area of either of the two congruent parallel faces of a prism; for a cylinder, area of the base = • height - the perpendicular distance to the base
• incline - the slant (to the right or left) or slope of a three-dimensional shape
• radius - the length of a line segment that connects the center of circle to any point on the circle
• cylinder - a three-dimensional geometric figure that has two congruent and parallel circular bases connected to a curved surface
• volume of a cylinder - (V: Volume; r: radius of the circular base and h: height of the cylinder)

### Tutorial Details

 Approximate Time 15 Minutes Pre-requisite Concepts Area formulas, area of the base, circles, cylinders, height, incline, volume of cylinders Course Algebra Foundations Type of Tutorial Dynamic Modeling Key Vocabulary area of the base, base, cylinder