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Section 9.4 Volume and Surface Area. What You Will Learn. Volume Surface Area. 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.

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## Section 9.4 Volume and Surface Area

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**What You Will Learn**• Volume • Surface Area**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.**Volume**• Solid geometry is the study of threedimensional solid figures, also called space figures. • Volumes of threedimensional figures are measured in cubic units such as cubic feet or cubic meters. • Surface areas of threedimensional figures are measured in square units such as square feet or square meters.**Figure**Formula Diagram Rectangular Solid V = lwh Cube V = s3 Cylinder V = πr2h Cone Sphere Volume Formulas h l w s s s r h h r**Figure**Formula Diagram Rectangular Solid SA=2lw + 2wh +2lh Cube SA= 6s2 Cylinder SA = 2πrh + 2πr2 Cone Sphere Surface Area Formulas h l w s s s r h r h r**Example 1: Volume and Surface Area**• Determine the volume and surface area of the following threedimensional figure. • Solution**Example 1: Volume and Surface Area**• Determine the volume and surface area of the following threedimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.**Example 1: Volume and Surface Area**• Solution**Example 1: Volume and Surface Area**• Determine the volume and surface area of the following threedimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.**Example 1: Volume and Surface Area**• Solution**Example 1: Volume and Surface Area**• Determine the volume and surface area of the following three-dimensional figure. When appropriate,use the πkey on yourcalculator and roundyour answer to thenearest hundredths.**Example 1: Volume and Surface Area**• Solution**Polyhedra**• A polyhedron is a closed surface formed by the union of polygonal regions.**Euler’s Polyhedron Formula**• Number of vertices number offaces number of edges = 2 + –**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: 4 faces, 4 vertices, 6 edges Cube: 6 faces, 8 vertices, 12 edges Octahedron: 8 faces, 6 vertices, 12 edges Dodecahedron: 12 faces, 20 vertices, 30 edges Icosahedron: 20 faces, 12 vertices, 30 edges**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.**Prism**• The prisms illustrated are all right prisms. • When we use the word prism in this book, we are referring to a right prism.**Volume of a Prism**• V = Bh, • where B is the area of the base and h is the height.**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 in3 to • a) determine the volume of the fish tank in cubic inches.**Example 6: Volume of a Hexagonal Prism Fish Tank**Solution Area of hexagonal base: two identical trapezoids Areabase = 2(96) = 192 in2**Example 6: Volume of a Hexagonal Prism Fish Tank**Solution Volume of fish tank:**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**Pyramid**• A pyramid is a polyhedron with one base, all of whose faces intersect at a common vertex.**Volume of a Pyramid**• where B is the area of the base and h is the height.**Example 8: Volume of a Pyramid**Determine the volume of the pyramid. Solution Area of base = s2 = 22 = 4 m2 The volume is 4 m3.

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