Section 9.4. Volume and Surface Area. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Transcription

1 Section 9.4 Volume and Surface Area

2 INB Table of Contents Date Topic Page # February 6, 2013 Area and Perimeter Table 36 February 6, 2013 Section 9.3 Notes 37 February 11, 2013 Volume and Surface Area Formulas 38 February 11, 2013 Section 9.4 Notes 39 February 11, 2013 Test #2 Practice Workspace 40 February 11, 2013 Test #2 Practice Test

3 What You Will Learn Volume Surface Area 9.4-3

4 Volume Volume is the measure of the capacity of a three-dimensional figure. It is the amount of material you can put inside a three-dimensional figure. Surface area is sum of the areas of the surfaces of a three-dimensional figure. It refers to the total area that is on the outside surface of the figure

5 Volume Solid geometry is the study of three-dimensional solid figures, also called space figures. Volumes is measured in cubic units such as cubic feet or cubic meters. Surface area is measured in square units such as square feet or square meters

6 9.4-6

7 Example 1: Volume and Surface Area Determine the volume and surface area of the following threedimensional figure. Solution V = lwh = = 198 ft 3 SA = 2lw + 2wh + 2lh = = = 234 ft

8 Example 1: Volume and Surface Area Determine the volume and surface area of the following threedimensional figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredths

9 Example 1: Volume and Surface Area Solution V = π r 2 h = π = 128π m 3 SA = 2π rh + 2π r 2 = 2π π 4 2 = 64π + 32π = 96π m

10 Example 1: Volume and Surface Area Determine the volume and surface area of the following threedimensional figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredths

11 Example 1: Volume and Surface Area Solution V = 1 π r 2 h = 1 π = 24π m 3 SA = π r 2 + π r r 2 + h 2 = π π = 9π + 3π m

12 Example 1: Volume and Surface Area Determine the volume and surface area of the following three-dimensional figure. When appropriate, use the π key on your calculator and round your answer to the nearest hundredths

13 Example 1: Volume and Surface Area Solution V = 4 π r 3 = 4 π = 972π cm 3 SA = 4π r 2 = 4 π 9 2 = 4 π 81 = 324π cm

14 Polyhedra A polyhedron is a closed surface formed by the union of polygonal regions

15 Euler s Polyhedron Formula Number number number of vertices of + edges of faces =

16 Prism The prisms illustrated are all right prisms. When we use the word prism in this book, we are referring to a right prism

17 Volume of a Prism V = Bh, where B is the area of the base and h is the height

18 Example 6: Volume of a Hexagonal Prism Fish Tank Frank Nicolzaao s fish tank is in the shape of a hexagonal prism. Use the dimensions shown in the figure and the fact that 1 gal = 231 in 3 to a) determine the volume of the fish tank in cubic inches

19 Example 6: Volume of a Hexagonal Prism Fish Tank Solution Area of hexagonal base: two identical trapezoids A = 1 h ( b + b ) trap A trap = 1 2 (8)(16 + 8) = 96 in2 Area base = 2(96) = 192 in

20 Example 6: Volume of a Hexagonal Prism Fish Tank Solution Volume of fish tank: V = B h = = 4608 in

21 Example 6: Volume of a Hexagonal Prism Fish Tank b) determine the volume of the fish tank in gallons (round your answer to the nearest gallon). Solution V = gal

22 Pyramid A pyramid is a polyhedron with one base, all of whose faces intersect at a common vertex

23 Volume of a Pyramid where B is the area of the base and h is the height. V = 1 3 Bh

24 Example 8: Volume of a Pyramid Determine the volume of the pyramid. Solution Area of base = s 2 = 2 2 = 4 m 2 V = 1 3 Bh = = 4 m 3 The volume is 4 m