Students observe the changes in the surface area of a cone when the height and the radius are changed.
After completing this tutorial, you will be able to complete the following:
A cone is a three-dimensional geometric figure
A cone is a shape whose base is a circle and whose sides taper up to a point.
In the diagram below, an arc can be identified between points B and C on the circumference of the circle. The shaded area represents a sector.
The surface area of a cone can be found by using the formula .
The surface area of a cone is equal to the sum of the area of the base and the lateral area. To find the surface area of a cone, first we need to calculate the area of the base. The area of the base is equal to .
Next, we find the lateral area, which is the sum of all its faces excluding the base. The lateral area is equal to the area of the sector, which would be .
To find the length of l (slant height), use the relation of the length of the arc BC and the circumference of the base. The length of arc BC is equal to the circumference of the base ( ).
At the same time, the length of the arc is equal to . Set these two equations equal to one another: . We find that . Now we can replace one l in the area of the sector formula to get , which simplifies to .
The area of the base of the cone is . So, the surface area of the cone is equal to .
This Activity Object will focus on the changes in a cone's surface area when other variables are altered. For instance, students will be able to change the height and radius of the cone, and then observe the results from these changes.
The area of the base of a cone is proportional to its radius squared.
The area of the base is equal to . The area of the cone's base increases as the radius increases and decreases as the radius does the same.
The lateral area of a cone changes when its radius or its height changes.
The lateral area increases when the radius or the height increases. Likewise, the lateral area decreases when the radius or height decreases.
The following key vocabulary terms will be used throughout this Activity Object:
|Approximate Time||20 Minutes|
|Pre-requisite Concepts||Students should know the definitions of circle, cone, slant height, and net, and be able to use formulas to determine the area of a circle, circumference of a circle, lateral area, and surface area.|
|Type of Tutorial||Skills Application|
|Key Vocabulary||area of base, cone, height|