7th Grade Math

The net shows that the surface area of a cone is the sum of its base B and its

lateral area L.A. The base B is a circle. The lateral area L.A. is part of a larger circle.

In the following Activity, you will determine the formula for the lateral surface

area of a cone.

Find the Surface Area of a Cone

Use a compass to draw a circle. It represents

$ = 2 πr

the lateral surface area.

Draw 3 diameter lines that divide the circle

equally into 6 sections.

Cut out the sections and form a figure that

resembles a parallelogram. 

the Results

1. The circumference of the circle is represented by 2πr. What expression
   represents the length of the parallelogram in Step 3?


2. MAKE A CONJECTURE Use the expression from Exercise 1 to write a
   formula for the area of the parallelogram, which is the lateral surface
   area of the cone.


3. MAKE A CONJECTURE Write a formula for the total surface area of a cone.


4. Why is only a portion of the larger circle necessary to construct a cone?


5. If the radius of the base is increased while the slant height stays the same,
   how will that affect the lateral surface area?


6. If a cone’s slant height is decreased, which would be affected more: the base
   or the lateral area? Justify your response.


7. Find the surface area of the party hat that Corinne is covering with tissue
   paper.

Lesson 2F Surface Area 599

 r

C = 2 πr C^ =^2 πr

r



B

L.A.

592_599_C10_L2_895130.indd 599 1/4/10 2:57 PM