Chapter 11: Measurement of Figures and Solids Part B
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1 Chapter 11: Measurement of Figures and Solids Part B Surface Area of Prisms & Cylinders What is surface area? Is it: Cushions on sofa being re-stuffed with material? Old sofa getting recovered? Manufacturer of paper bags must determine cost of paper to make bags? Cement manufacturer must determine how much cement one bag holds? Designer decides how much wallpaper is needed in a room? Prism: Cylinder: Lateral area: Surface area:
2 Formulas The surface area of any prism or cylinder is the sum of its lateral area and twice the area B of the base: Prisms Cylinders SA = LA + 2B SA = LA + 2B = = = Example 1: Find the surface area of the figures below Example 2: Find the surface area of each solid
3 Surface Area of Pyramids & Cones Pyramid: Cone: Formulas The surface area for a pyramid or cone is the sum of the lateral area plus the area of the base. SA = LA + B SA = LA + B = = = =
4 Example 1: Find the surface area of each pyramid or cone below Example 2: A pile of sand has been stored in the shape of a cone. The yard- keeper knows the pile is 20 ft tall and 102 ft in circumference at the base. What is the area of the conical tarpaulin needed to cover the pile? 11.6 Volume of Prisms & Cylinders Volume:
5 Example 1: Find the volume of the puzzle piece in cubic units Volume Formulas Example 2: Find the volume of each solid. 1. Right Trapezoidal Prism 2. Right Cylinder
6 Example 3: 1. The volume of a cube is 90 in Find the length x using the given Find the value of x. volume V. V = 128π cm 3 Even though all 3 have different shaped bases or may be oblique, since each cross section has the same area and height, each figure has the same volume. Example 4: 1. Find the volume of the oblique cylinder. 2. Find the volume of the oblique prism.
7 Example 5: Find the volume of the solid shown below Volume of Pyramids & Cones Density: Density = A piece of copper has a volume of 8.25 cm 3 and a mass of grams. What is the density of copper? Gold has a density of 19.3 g/cm 3. Cody has a piece of metal that looks like gold. It has a volume of 15.3 cm 3 and a mass of grams. Is it real gold or Fool s Gold? Recall that the volume for a prism is Bh, where B is the area of the base and h is the height. Is the volume of a pyramid more or less than the prism? About how much?
8 Example 1: Find the volume of the solid Example 2: Originally, Khafre s pyramid had height 144 meters and volume 2,226,450 m 3. Find the side length of the square base.
9 Example 3: Find the volume of the solid Example 4: Find the volume of the solid shown
10 11.8 Surface Area & Volume of Spheres Sphere: Radius: Chord: Diameter: Surface Area I bet you have always wondered how they get the surface area of a sphere! Well.here s a good way how to picture how they get it. Think of a baseball! The surface of a baseball is sewn from 2 congruent shapes. Each resembles 2 joined circles So with approximately 4 circles, and with radius r and the area of a circle A = πr², we have: Example 1: 1. Find the surface area of the sphere. 2. The surface area of a sphere is 40.96π in 2. What is the diameter?
11 Circles, Great Circles, Hemispheres Great circle: Hemisphere: Volume How d They Get That? Imagine that the interior of a sphere radius r is n pyramids - each have base area B and height r. Volume(Sphere) n(volume of pyramids) n( 1 3 Br) 1 3 nbr Each pyramid has volume of 1 3 Br Regrouping 1 (4πr²)r Substitute 4πr² for nb (SA of a sphere) πr³ Simplifying Example 2: Find the volume of the soccer ball with diameter 9 inches.
12 Composite Solids Find the volume of the composite solid Explore Similar Solids Similar solids: The is called the scale factor of one solid to the other solid. Any two cubes are similar, as well as any two spheres. Example 1: Tell whether right cylinder P is similar to right cylinder A or right cylinder B. Explain your reasoning.
13 Example 2: The beach balls shown are similar with a scale factor of 7:6. Find the surface area and volume of the smaller ball given that the larger ball has a surface area of in 2 and a volume of in 3. Example 3: The cones are similar. Cone A has a volume of 125 m 3 and cone B has a volume of 512 m 3. Find the scale factor of cone A to cone B. Example 4: A garden store sells gravel in boxes that are cubes. The edge of the smaller cube, which sells for $40 is threefourths of the edge of the larger cube, which sells for $ Which box is the better buy?
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