11.2 and11.4 Surface Area and Volume Prisms
-
Upload
jtentinger -
Category
Documents
-
view
898 -
download
1
Transcript of 11.2 and11.4 Surface Area and Volume Prisms
S
Chapter 11 Surface Area and Volume
11.2 and 11.4
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
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
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
Euler’s Formula
# Faces + # Vertices = # Edges + 2
Cross Section
The intersection of a solid and a plane.
A slice of the solid
What is the cross section formed?
Prisms
Prism: polyhedron with two congruent, parallel faces, called bases
Lateral faces: all the other faces
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)
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
What is the Surface Area?
What is the Surface Area? Lateral Area?
Volume of a Prism
Volume = Base times height
V = Bh
Cylinder
Two congruent, parallel bases that are circles
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
Volume of a Cylinder
Volume = Base times height
V = Bh
V = πr2h
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
Homework
Pg. 704
#10 – 20 even, 26 (8 problems)
Pg. 721
#6 – 20 even, 38 (9 problems)
17 total problems