Reteaching. Solids. These three-dimensional figures are space figures, or solids. A cylinder has two congruent circular bases.
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1 9- Solids These three-dimensional figures are space figures, or solids A B C D cylinder cone prism pyramid A cylinder has two congruent circular bases AB is a radius A cone has one circular base CD is a diameter A prism has two bases that are congruent and parallel The lateral faces are parallelograms A pyramid has one base The lateral faces are triangles The shape of a base is used to name the solid A triangular prism and a square pyramid are shown above For each figure, describe the base(s) and name the figure For the figure, name a pair of parallel lines and a pair of intersecting lines 7 A F B E C D Course Lesson 9-
2 9-2 Volume of Prisms and Cylinders To find the volume of a prism or a cylinder, multiply the base area B and the height h Find the base area B 2 Multiply base area B and height h V l = 6 yd r = yd h = 5 yd w = yd h = 0 yd Find the base area and volume of each prism 2 cm 7 cm 5 cm B B B V V V Find the base area of each cylinder to the nearest hundredth Then find the volume of each cylinder to the nearest cubic unit cm 5 6 cm B w V yd 2 20 yd 8 ft The volume is 20 yd B pr 2 V p yd yd yd The volume is about 28 yd 8 m 8 in 6 m m 2 in B B B V V V Course Lesson 9-2
3 9- Volumes of Pyramids and Cones To find the volume of a pyramid or cone, multiply, the base area B, and the height h Find the base area B 2 Multiply, the base area B, and the height h V 9 cm 6 cm Find the volume of each figure to the nearest whole cubic unit 2 2 cm 2 cm cm 2 m 8 m cm 5 cm 2 m B w V 6 (2)(9) 2 cm 2 72 cm B = pr 2 p cm 2 The volume is 72 cm V (2826)(2) 0 cm The volume is about cm 6 cm 58 cm 0 cm cm 5 Find the height of a cone with an approximate volume of cm and a radius of cm 6 cm Course Lesson 9-
4 9- Spheres Find the surface area and volume of a beach ball with a radius of 8 inches The surface area of a sphere is four times the product of p and the square of the radius r SA = pr 2 Surface area of a sphere = p(8 2 ) Substitute = 256p Simplify < 80 Use a calculator The surface area of the beach ball is about 80 in 2 The volume of a sphere is four-thirds of the product of p and the radius r cubed V = pr Volume of a sphere = p(8 ) Substitute 2,08 = p Simplify 2,5 Use a calculator The volume of the beach ball is about 25 in A glass blower sells opalescent glass spheres Find the surface area and volume of each sphere to the nearest whole number blue: r = 2 in 2 green: d = 9 cm yellow: d = 6 in multicolored: r = 5 in 5 clear: r = 6 cm 6 opaque: d = 85 in Course Lesson 9-
5 9-5 Exploring Similar Solids Two solids are similar solids if they have the same shape and all of their corresponding lengths are proportional A special relationship exists among the measures of similar solids: The ratios of the corresponding dimensions of similar solids is a b The ratio of their surface areas is a 2 The ratio of their volumes is Example: Two similar cylindrical watering cans have diameters of in and 8 in Find the volume of the larger watering can if the volume of the smaller watering can is 882 in Write the ratio of corresponding dimensions, so the ratio of the volumes is a, or b volume of small watering can 2 Write a proportion: volume of large watering can x x = (882)(729) d Substitute the known volume d Cross multiply x = 62,978 d Divide both sides by x =,8757 d Simplify The volume of the larger watering can is about,875 in For each pair of similar solids find the value of the variable A triangular prism has a height of 8 cm, surface area of 6 cm 2, and volume of 279 cm Find the surface area and volume of a similar prism with a height of 2 cm Round your answers to the nearest whole number x a b b 2 8 x 5 A rectangular prism has a height of 2 inches, a surface area of,088 in 2 and a volume of 2,2 in Find the surface area and volume of a similar prism with a height of 6 in 2 Course Lesson 9-5
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Name: Class: Date: ID: A 3D Object Unit Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A rectangular prism has a volume of 3x 2 + 18x + 24. Its
2. a. approximately cm 3 or 9p cm b. 20 layers c. approximately cm 3 or 180p cm Answers will vary.
Answers Investigation ACE Assignment Choices Problem. Core Other Connections Problem. Core,, Other Applications 7, ; Connections 7 0; unassigned choices from previous problems Problem. Core 7 Other Connections,