The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net.

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1 The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid figure is laid out flat showing each face of the figure.

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3 Color a Rectangular Prism Net 1. Color the rectangular prism like the example below: (Blue, Pink, Green)

4 Create a Rectangular Prism Net 1. Cut out the rectangular prism net along the solid black outside line. 2. DO NOT cut off the flaps. 3. Fold along the dotted lines. Make sure you make a good STRAIGHT crease. 4. Find the surface area of each rectangle and write it on the back of each rectangle. 5. Find the total surface area and write it the table.

5 Surface Area Table Faces Surface Area cm² Green Face 1 Green Face 2 Pink Face 1 Pink Face 2 Blue Face 1 Blue Face 2 Total

6 10-8 Finding Insert Lesson Volume Title Here volume Vocabulary

7 Volume is the number of cubic units needed to fill a space.

8 # of cubes in a Rectangular Prism 6. Lay the rectangular prism face down, so that the folds fold up. 7. Lay 1 layer of cubes down. 8. How many cubes fit on the first layer? Fill in your answer. 9. Start the 2 nd layer of cubes & fill in your answer. # of cubes in Layer 1: # of cubes in Layer 2:

9 Volume of Rectangular Prism 10. How many layers can you fit? 11. The number of layers is the height. Write in your answer. 12. What is the total volume of the rectangular prism? Write in your answer. 13. Can you think of a formula that we can use EVERY time so that we don t have to do this much work when we want to find the volume of a prism?

10 It takes 10, or 5 2, centimeter cubes to cover the bottom layer of this rectangular prism. There are 3 layers of 10 cubes each. It takes 30, or 5 2 3, cubes to fill the prism. The volume of the prism is 5 cm 2 cm 3 cm = 30 cm 3.

11 Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. 13 in. V = lwh 26 in. 11 in. Write the formula. V = l = 26; w = 11; h = 13 V = 3,718 in 3 Multiply.

12 Try This: Example 1 Find the volume of the rectangular prism. 16 in. V = lwh 29 in. 12 in. Write the formula. V = l = 29; w = 12; h = 16 V = 5,568 in 3 Multiply.

13 To find the volume of any prism, you can use the formula V= Bh, where B is the area of the base, and h is the prism s height. So, to find the volume of a triangular prism, B is the area of the triangular base and h is the height of the prism.

14 Additional Example 2A: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. A. V = Bh V = ( ) 4 2 V = m 3 Write the formula. B = ; h = 4. 2 Multiply.

15 Additional Example 2B: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. B. V = Bh V = ( ) 6 2 V = ft 3 Write the formula. B = ; h = 6. 2 Multiply.

16 Try This: Example 2A Find the volume of each triangular prism. A. 1.6 m 7 m 4.2 m V = Bh 1 V = ( ) 7 2 V = m 3 Write the formula. B = ; h = 7. 2 Multiply.

17 Try This: Example 2B Find the volume of each triangular prism. B. 9 ft 4.5 ft V = Bh V = ( ) 5 2 V = ft 3 5 ft Write the formula. B = ; h = 5. 2 Multiply.

18 Additional Example 3: Problem Solving Application Suppose a facial tissue company ships 16 cubic tissue boxes in each case. What are the possible dimensions for a case of tissue boxes? 1 Understand the Problem The answer will be all possible dimensions for a case of 16 cubic boxes. List the important information: There are 16 tissue boxes in a case. The boxes are cubic, or square prisms.

19 Additional Example 3 Continued 2 Make a Plan You can make models using cubes to find the possible dimensions for a case of 16 tissue boxes.

20 Additional Example 3 Continued 3 Solve You can make models using cubes to find the possible dimensions for a case of 16 cubes. The possible dimensions for a case of 16 cubic tissue boxes are the following: , 1 2 8, 1 4 4, and

21 Additional Example 3 Continued 4 Look Back Notice that each dimension is a factor of 16. Also, the product of the dimensions (length width height) is 16, showing that the volume of each case is 16 cubes.

22 Try This: Example 3 Suppose a paper company ships 12 cubic boxes of envelopes in each case. What are the possible dimensions for a case of envelope boxes? 1 Understand the Problem The answer will be all possible dimensions for a case of 12 cubic boxes. List the important information: There are 12 envelope boxes in a case. The boxes are cubic, or square prisms.

23 Try This: Example 3 Continued 2 Make a Plan You can make models using cubes to find the possible dimensions for a case of 12 boxes of envelopes.

24 Try This: Example 3 Continued 3 Solve You can make models using cubes to find the possible dimensions for a case of 12 cubes. The possible dimensions for a case of 24 cubic envelope boxes are the following: , 1 2 6, 1 3 4, and

25 Try This: Example 3 Continued 4 Look Back Notice that each dimension is a factor of 12. Also, the product of the dimensions (length width height) is 12, showing that the volume of each case is 12 cubes.

26 10-8 Finding Insert Lesson Volume Title Here Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 3,600 cm 3 2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm cm 3 3. Find the volume of the figure shown cm 3

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