Lesson 1

Connect

 

Going Beyond

 

The surface area of a cone can also be determined by finding the area for each shape in the cone's net. The area formulas for the shapes in the net are used to develop the surface area formula for the cone. The formula for the surface area of a cone is developed below.

 

You may find it helpful to have a 3-D model of a cone as you work through the following steps. You can print the net of a cone to help build your 3-D model.

 

Call the radius of the cone’s circular base r and the slant height of the side h. The slant height is measured along the cone’s surface from the base to the top of the cone.

 

Now compare your 3-D cone to its net.

 

 

Look at the net. The red portion of the large circle is the surface of the cone.

 

The large circle of radius s has a circumference of and an area of .

 

But part of that circle is missing!

 

The part of the large circle coloured red is formed from an arc that is exactly as long as the circumference of the small circle. The circumference of the small circle is .

 

Now look at the circumference of the large circle. Compare the red part of the circumference to the whole circumference. You find the following fraction.

 

 

You can use this ratio to calculate the area of the red portion of the cone to be

 

  So, the surface area of the cone = area of the conical side + area of the circular base.

 

 

Project Connection

 

The Module 6 Project is actually a combined project for Modules 6 and 7. Take some time to familiarize yourself with the project goals and requirements. You will begin working on the project steps in Lesson 4 or when you feel comfortable with surface area.

 

Lesson 1 Assignment