11.3 and11.5 surface area and volume pyramids
TRANSCRIPT
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S
Chapter 11 Surface Area and Volume
11.3 and 11.5
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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
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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
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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
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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
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What is the Surface Area
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What is the lateral area?
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Volume of a Pyramid
V = 1/3 Bh
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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
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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
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What is the surface area in terms of pi?
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Volume of a Cone
V = 1/3Bh
V = 1/3 π r2 h
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Homework
Pg. 713
#10 – 22 even, 28 (8 problems)
Pg. 729
#6 – 18 even, 30 (8 problems)
16 problems total