MATHEMATICS MAT1L. Grade 9, Essentials
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1 MATHEMATICS MAT1L Grade 9, Essentials
2 Volume Lesson 16
3 Lesson Sixteen Concepts Explore and describe situations from everyday life and the workplace that require calculating or measurement of volume. Investigate the volume of a variety of prism whose bases involve rectangular regions. Predict and explain, from investigations involving the building of prisms, that the volume of a prism is given by multiplying the area of its base by its height. Estimate and calculate the volumes of rectangular prisms drawn from applications in everyday life and the workplace. Select the most appropriate standard unit to measure volume of a figure. Solve problems involving volume in applications drawn from everyday situations. Organize measurement information, using a simple framework Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of investigations, using appropriate terminology, symbols and form. Volume Volume is the amount of space an object occupies. Number of cubes in one layer Number of layers Volume = 12 cm 2 x 5 cm = 60 cm Copyright 2005, Durham Continuing Education Page of 47
4 Example Find the volume of the rectangular prism given below. a. Answer: Volume = Area of base x Height = 8 m x 7 m x 5 m 2 = 56 m x 5 m Find the area of the base and multiply that answer by the height of the prism. Example Volume always has its units to = 280 m the exponent of. Estimate then find the volume of the rectangular prism given below. b. Estimated Answer: Volume = Area of base x Height = 2 m x 2 m x 1.5 m = 4 m 2 x 1.5 m = 6 m Answer: Volume = Area of base x Height = 2. m x 2.1 m x 1.6 m 2 = 4.8 m x 1.6 m = m Copyright 2005, Durham Continuing Education Page 4 of 47
5 Example Find the volume of the object given below. c. Answer: V1 = Area of base x Height V2 = Area of base x Height = 7 cm x 6 cm x 5 cm = 2.2 cm x 2.1 cm x 2 cm 2 2 = 42 cm x 5 cm = 4.62 cm x 2 cm = 210 cm = 9.24 cm Total Volume = V1 + V2 = = cm Copyright 2005, Durham Continuing Education Page 5 of 47
6 Support Questions 1. Estimate then calculate the volume for each of the following objects. a. b. 1. Estimate then calculate the volume of the object below. 2. Find the volume of the rectangular prism for each of the following: a. length 5 cm, width 7 cm, height 4 cm b. dimensions 25 m by 10 m by 50 m 2 c. area of base 70 mm, height 10 mm Copyright 2005, Durham Continuing Education Page 6 of 47
7 Support Questions (con t). Use the diagram provided to answer the following questions. a) Find the amount of space occupied by the freezer. b) Find the volume of the inside of the freezer if each side is 6 cm thick. 5. Copy and complete the chart for rectangular prisms. Length Width Height Volume 10 cm 8 cm 720 cm m 5 m 120 m 14 mm 7 mm 980 mm Key Question #16 1. Estimate then calculate the volume for each of the following objects. a) b) Copyright 2005, Durham Continuing Education Page 7 of 47
8 2. Estimate then calculate the volume of the object below.. Find the volume of the rectangular prism for each of the following: a. length cm, width 10 cm, height 5 cm b. dimensions 15 m by 7 m by m 2 c. area of base 48 mm, height 9 mm 4. Use the diagram provided to answer the following questions. a. Find the amount of space occupied by the filing box. b. Find the volume of the inside of the box if each side is 1 cm thick. 5. Copy and complete the chart for rectangular prisms. Length Width Height Volume 5 cm 15 cm 75 cm 9 m 4 m 162 m 19 mm 2.5 mm mm 6. What units would you use to find the volume of an above ground swimming pool? Explain your reasoning. 7. Describe two situations from everyday life and/or the workplace that requires calculating and measuring of volume. Copyright 2005, Durham Continuing Education Page 8 of 47
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