11.2 and11.4 surface area and volume prisms
TRANSCRIPT
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S
Chapter 11 Surface Area and Volume
11.2 and 11.4
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Essential Understanding
You can analyze a 3D figure by using the relationship among its vertices, edges, and faces
To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figure
You can find the volume of a prism or cylinder when you know its height and the area of its base
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Objectives
Students will be able to recognize polyhedra and their parts Visualize cross sections of space figures Find the surface area of a prism and a cylinder Find the volume of a prism and the volume of a
cylinder
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Polyhedron
A space figure, or 3D figure whose surfaces are polygons
Face: each polygon
Edge: segment formed by the intersection of two faces
Vertex: point where three or more edges intersect
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Euler’s Formula
# Faces + # Vertices = # Edges + 2
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Cross Section
The intersection of a solid and a plane.
A slice of the solid
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What is the cross section formed?
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Prisms
Prism: polyhedron with two congruent, parallel faces, called bases
Lateral faces: all the other faces
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Prisms…
Right prism: the lateral faces are rectangles and a lateral edge is an altitude
Oblique Prism: some or all of the lateral faces are nonrectangular.
(For this chapter, assume that a prism is a right prism unless otherwise stated)
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LA and SA of a Prism
Lateral Area (LA): sum of the areas of the lateral faces LA = ph
Surface Area (SA): sum of the lateral area and the area of the two bases SA = LA + 2B
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What is the Surface Area?
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What is the Surface Area? Lateral Area?
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Volume of a Prism
Volume = Base times height
V = Bh
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Cylinder
Two congruent, parallel bases that are circles
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LA and SA of a Cylinder
Lateral Surface Area (LA): circumference of the base and the height of the cylinder LA = 2πr * h
OR LA = πdh
Surface Area (SA): Sum of the lateral surface area the two bases SA = LA + 2B SA = 2πrh + 2πr2
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Volume of a Cylinder
Volume = Base times height
V = Bh
V = πr2h
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Composite Space Figure
3D figure that is a combination of two or more simpler figures
To find the volume of a composite space figure, add the volumes of the figures that are combined
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Homework
Pg. 704
#10 – 20 even, 26 (8 problems)
Pg. 721
#6 – 20 even, 38 (9 problems)
17 total problems