The relationship among the height, radius, and surface areas of a cylinder is observed.
After completing this tutorial, you will be able to complete the following:
A right cylinder is a three-dimensional geometric figure.
A right cylinder has two congruent and parallel bases in which the centers of the bases are aligned directly one above the other. The bases do not have to be circles. If the bases are circles, then it is called a right circular cylinder.
In the Activity Object, right circular cylinder are used, however, they may also simply be called cylinders.
The surface area of a cylinder can be found by using the formula .
The surface area of a cylinder is equal to the sum of the area of the bases and the lateral area. To find the surface area of a cylinder, first we need to calculate the area of the bases. The area of the bases is equal to . Next, we find the lateral area, which is the sum of all its faces excluding the bases. The lateral area is equal to the product of the length ( ) and the width (h) of the rectangle. So the surface area of the cylinder is equal to .
This Activity Object will focus on the changes in a cylinder's surface area when other variables are altered. For instance, students will be able to change the height and radius of the cylinder, and then observe the results from these changes.
The area of the base of a cylinder is proportional to its radius squared.
The area of the bases is equal to . The area of the cylinder's bases increases as the radius increases and decreases as the radius does the same.
The lateral area of a cylinder is proportional to both its radius and its height.
The lateral area of a cylinder is equal to .
The following key vocabulary terms will be used throughout this Activity Object:
(SA: surface area, r: radius and h: height)
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Students should know how to calculate the area of a circle and the lateral and surface areas of a cylinder, and be able to recognize a cylinder|
|Type of Tutorial||Skills Application|
|Key Vocabulary||area of the base, base, circumference|