S Chapter 11 Surface Area and Volume 11.3 and 11.5
May 25, 2015
S
Chapter 11 Surface Area and Volume
11.3 and 11.5
Essential Understanding
To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figure
The volume of a pyramid is related to the volume of a prism with the same base and height
The volume of cone is related to the volume of a cylinder with the same base and height
Objectives
Students will be able to Find the surface area of a pyramid and a cone Find the volume of a pyramid and of a cone
Pyramids
Pyramid: polyhedron in which one face (the base) can be any polygon and the other faces (lateral faces) are triangles
Vertex: top of pyramid Slant height: length of the altitude of a lateral face of the
pyramid Assume a pyramid is a regular pyramid unless otherwise
stated
LA and SA of Pyramids
Lateral Area (LA): sum of the areas of the congruent lateral faces Half the product of the perimeter and the
slant height LA = ½ p l
Surface Area (SA): add the area of the base to the lateral area. SA = LA + B SA = ½ p l + B
When the slant height is not given you mustfind it first in order to find the LA or the SA
What is the Surface Area
What is the lateral area?
Volume of a Pyramid
V = 1/3 Bh
Cone
Base is a circle
Right Cone: altitude is a perpendicular segment form the vertex to the center of the base
Height is the altitude
Slant Height: distance from the vertex to a point on the edge of the base
LA and SA of a Cone
Lateral Area (LA): half the product of the circumference of the base and the slant height ½ * 2πr * l = π r l
Surface Area (SA): sum of the lateral area and the base LA + B π r l + πr2
What is the surface area in terms of pi?
Volume of a Cone
V = 1/3Bh
V = 1/3 π r2 h
Homework
Pg. 713
#10 – 22 even, 28 (8 problems)
Pg. 729
#6 – 18 even, 30 (8 problems)
16 problems total