Section 12.3 ~ Surface Area of Pyramids and Cones
Topics in this lesson:
• pyramid
• vertex of a pyramid/cone
• regular pyramid
• slant height
• cone
• right cone
• lateral surface
• surface area of a cone/pyramid
Objective: To be able to find the surface
area of a pyramid and cone.
Vocabulary
pyramid ­ a polyhedron with a polygon base and lateral faces that are triangles vertex of a pyramid ­ the common vertex of the lateral faces
regular pyramid ­ 1. regular polygon for a base
2. lateral faces are congruent isosceles triangles
3. upright (no lean or tilt)
slant height ­ the height of a lateral face of the regular pyramid *Refer to your Words to Review if you have questions on these. Example 1
Find the area of each lateral face of the regular square pyramid.
.
Surface Area of a Regular Pyramid
The surface area SA of a regular pyramid is:
SA = B = base
P = perimeter
l = slant height
Example 2
Example 3
Find the surface area of the regular hexagonal pyramid.
Find the surface area of the regular square pyramid.
.
Vocabulary
cone ­ a circular base and a vertex that is not in the same plane as the base
vertex of a cone ­ the point on the cone that is located at a perpendicular distance from the base, called the height of the cone
right cone ­ upright (no lean or tilt)
lateral surface of a cone ­ everything but the base
Surface Area of a Right Cone
The surface area SA of a right cone is:
SA = Example 4
Find the lateral area and surface area of the right cone.
Example 5
A carpenter uses a weight in the shape of a right cone to identify vertical lines. The cone has a radius of 6.5 mm and a height of 13 mm. Find the approximate lateral area of the weight.
12.3 Assignment
p. 814, #4-8, 10, 12, 13-20, 22-24