1. Everything you need to know about CONES
By: the students in group 2

2. What is in this presentation?
Examples of Cones and Definition
Examples of Cones in the real world
Definitions of surface area and volume
Formulas for surface area and volume
How to find surface area and volume

3. What do you need to do?
Fill in the notes that are provided to go with the presentation
Ask questions as needed for understanding
Make sure that you can answer each unit question specifically for a cone
Make any additional notes or comments on a separate sheet of paper

4. What is a cone?
A cone is a three-dimensional figure that has a circular base and a vertex point not in the same plane of the circle. The altitude is the perpendicular segment from the vertex to the center of the base. The height is the length of the segment while the slant height (of a right cone) is the distance from the vertex to the edge of the base.
h is height, r is radius, l is slant height
Faces, edges, and vertices does not apply to cones because it is not a polyhedron. A cone has no surfaces that are polygons.

5. Pictures in the real world
Ice Cream Cone
Tornado
Cones in traffic

6. What is Surface Area?
The definition of surface area is the sum of all unit squares that fit on the exterior of a solid.

7. The formula for Surface Area of a Cone2
SA = rl + r
SA = surface area
r = radius
l = slant height

8. Surface Area Example: SA = πrl + πr 2 How to work it out:
Plug in what you know
r = l = 8
SA = π(3)(8) + π (3)
Follow the order of operations
to simplify
SA = π(24) + π (9)
= 33 π ft squared
(left in terms of pi)
= 33(3.14)
= ft squared
(rounded to nearest tenth)
8 ft 2
6ft
The diameter goes all the way across. It is 6 ft. So half it to get the radius. r = 3

9. Another Surface Area Example: (slant height not given)
SA = πrl + πr 2 l
Now plug in what you know and simplify
SA = π(3)(5) + π(3)
= π(15) + π(9)
= 24π cm squared
= 75.4 cm squared 2
4 cm
3cm
We do not know the slant height. We have to find it using the pythagorean theorem.
a^2 + b^2 = c^ = l^2
3^2 + 4^2 = l ^ l = 5
= l ^2

10. What is Volume?
The amount of 3-dimensional space an object occupies. Capacity.

11. Formula for volume of a cone:2
V = 1/3πr h
V= volume
r = radius
h = height

12. Volume Example: V = 1/3πr h Plug in what you know and simplify2
V = 1/3πr h
Plug in what you know and simplify
V = 1/3π(6) (8)
= 1/3π(36)(8)
= 1/3π(288)
= 96π ft squared or
= 96(3.14)
= ft squared
Note:
Multiplying by 1/3 is the same as dividing by 3. 2
8 ft
12ft

13. Another Volume Example: (slant height given)
V = 1/3πr h 2 5
Now plug in what you know and simplify
V = 1/3π(3) (4)
= 1/3π(36)
= 12π cm squared
= 12(3.14)
= 37.7 cm squared 2 h
3cm
We do not know the height. We have to find it using the pythagorean theorem.
a^2 + b^2 = c^ h^2 = 16
3^2 + h^2 = 5 ^ h = 4
9 + h^2 = 25

14. Questions:
Do you (the audience) have any questions?

15. References
Bass, Laurie E, Charles, Randall I., Johnson, Art, and Kennedy, Dan. Geometry. Needham, MA: Prentice Hall, 2004.
“Cones.” Transtutors.com. 17 June 2009
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Karadimos, Mark. “Surface Area of Common Solids.” Mathguide. 19 September June 2009.
Pierce, Rod. "Definition of Volume" Math Is Fun. Ed. Rod Pierce. 11 Oct Jun