Section 9 4 Volume and Surface Area Copyright

Section 9. 4 Volume and Surface Area Copyright 2013, 2010, 2007, Pearson, Education, Inc.

What You Will Learn Volume Surface Area 9. 4 2 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 9. 4 3 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Volume Solid geometry is the study of three dimensional solid figures, also called space figures. Volumes of three dimensional figures are measured in cubic units such as cubic feet or cubic meters. Surface areas of three dimensional figures are measured in square units such as square feet or square meters. 9. 4 4 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Volume Formulas Figure Rectangular Solid Cube Cylinder Formula V = lwh Diagram h l V= s 3 V = π r 2 h w s s s r h Cone h Sphere 9. 4 5 r Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Surface Area Formulas Figure Formula Diagram Rectangular SA=2 lw + 2 wh +2 lh l Solid Cube SA= 6 s 2 s Cylinder SA = 2πrh + 2πr 2 Cone h h r Copyright 2013, 2010, 2007, Pearson, Education, Inc. w s s r Sphere 9. 4 6 r h

9. 4 7 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Volume and Surface Area Determine the volume and surface area of the following three dimensional figure. Solution 9. 4 8 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 9. 4 9 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Volume and Surface Area Solution 9. 4 10 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 9. 4 11 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Volume and Surface Area Solution 9. 4 12 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 9. 4 13 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 1: Volume and Surface Area Solution 9. 4 14 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Polyhedra A polyhedron is a closed surface formed by the union of polygonal regions. 9. 4 15 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Euler’s Polyhedron Formula number Number of of of + – = 2 faces edges vertices 9. 4 16 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Platonic Solid A platonic solid, also known as a regular polyhedron, is a polyhedron whose faces are all regular polygons of the same size and shape. There are exactly five platonic solids. Tetrahedron: Cube: Octahedron: Dodecahedron: Icosahedron: 4 faces, 6 faces, 8 faces, 12 faces, 20 faces, 4 vertices, 6 edges 8 vertices, 12 edges 6 vertices, 12 edges 20 vertices, 30 edges 12 vertices, 30 edges 9. 4 17 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Prism A prism is a special type of polyhedron whose bases are congruent polygons and whose sides are parallelograms. These parallelogram regions are called the lateral faces of the prism. If all the lateral faces are rectangles, the prism is said to be a right prism. 9. 4 18 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Prism The prisms illustrated are all right prisms. When we use the word prism in this book, we are referring to a right prism. 9. 4 19 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Volume of a Prism V = Bh, where B is the area of the base and h is the height. 9. 4 20 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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. 9. 4 21 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 6: Volume of a Hexagonal Prism Fish Tank Solution Area of hexagonal base: two identical trapezoids Areabase = 2(96) = 192 in 2 9. 4 22 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 6: Volume of a Hexagonal Prism Fish Tank Solution Volume of fish tank: 9. 4 23 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

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 9. 4 24 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Pyramid A pyramid is a polyhedron with one base, all of whose faces intersect at a common vertex. 9. 4 25 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Volume of a Pyramid where B is the area of the base and h is the height. 9. 4 26 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 8: Volume of a Pyramid Determine the volume of the pyramid. Solution Area of base = s 2 = 22 = 4 m 2 The volume is 4 m 3. 9. 4 27 Copyright 2013, 2010, 2007, Pearson, Education, Inc.