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**HOMEWORK & Learning Goal**

10-8 Finding Volume Course 1 HOMEWORK & Learning Goal 10-7 Lesson Quiz Lesson Presentation

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**Insert Lesson Title Here**

Course 1 10-7 Surface Area Insert Lesson Title Here Lesson Quiz Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft2 188.4 ft2 208 ft2

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Course 1 10-7 Surface Area 6th HOMEWORK Answers Page 532 #1-6

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Course 1 10-8 Finding Volume 6th Grade Math HOMEWORK Page 536 #1-6

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Our Learning Goal Students will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface area and volume of 3D shapes.

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**Our Learning Goal Assignments**

Learn to find the perimeter and missing side lengths of a polygon. Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms. Learn to break a polygon into simpler parts to find its area. Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure. Learn to identify the parts of a circle and to find the circumference and area of a circle. Learn to name solid figures. Learn to find the surface areas of prisms, pyramids, and cylinders. Learn to estimate and find the volumes of rectangular prisms and triangular prisms. Learn to find volumes of cylinders.

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**Today’s Learning Goal Assignment**

Course 1 10-8 Finding Volume Today’s Learning Goal Assignment Learn to estimate and find the volumes of rectangular prisms and triangular prisms.

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**Finding Volume 10-8 Warm Up**

Course 1 10-8 Finding Volume Warm Up Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 8 in., width 6 in., and height 12 in. 432 in2 2. cylinder with diameter 8 ft and height 5 ft ft2

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**Finding Volume 10-8 Problem of the Day**

Course 1 10-8 Finding Volume Problem of the Day A rectangular park is bordered by a 3-foot-wide sidewalk. The park, including the sidewalk, measures 125 ft by 180 ft. What is the area of the park, not including the sidewalk? 20,706 ft2

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**Insert Lesson Title Here**

Course 1 10-8 Finding Volume Insert Lesson Title Here Vocabulary volume

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

Course 1 10-8 Finding Volume Volume is the number of cubic units needed to fill a space.

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Course 1 10-8 Finding Volume 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 cm3.

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**Additional Example 1: Finding the Volume of a Rectangular Prism**

Course 1 10-8 Finding Volume Additional Example 1: Finding the Volume of a Rectangular Prism Find the volume of the rectangular prism. 13 in. 11 in. 26 in. V = lwh Write the formula. V = 26 • 11 • 13 l = 26; w = 11; h = 13 V = 3,718 in3 Multiply.

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**Finding Volume 10-8 Try This: Example 1**

Course 1 10-8 Finding Volume Try This: Example 1 Find the volume of the rectangular prism. 16 in. 12 in. 29 in. V = lwh Write the formula. V = 29 • 12 • 16 l = 29; w = 12; h = 16 V = 5,568 in3 Multiply.

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Course 1 10-8 Finding Volume 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.

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**Additional Example 2A: Finding the Volume of a Triangular Prism**

Course 1 10-8 Finding Volume Additional Example 2A: Finding the Volume of a Triangular Prism Find the volume of each triangular prism. A. V = Bh Write the formula. V = ( • 3.9 • 1.3) • 4 1 2 __ B = • 3.9 • 1.3; h = 4. 1 2 __ V = m3 Multiply.

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**Finding Volume 10-8 Try This: Example 2A**

Course 1 10-8 Finding Volume Try This: Example 2A Find the volume of each triangular prism. A. 7 m 1.6 m 4.2 m V = Bh Write the formula. V = ( • 4.2 • 1.6) • 7 1 2 __ B = • 4.2 • 1.6; h = 7. 1 2 __ V = m3 Multiply.

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**Additional Example 2B: Finding the Volume of a Triangular Prism**

Course 1 10-8 Finding Volume Additional Example 2B: Finding the Volume of a Triangular Prism Find the volume of the triangular prism. B. V = Bh Write the formula. V = ( • 6.5 • 7) • 6 1 2 __ B = • 6.5 • 7; h = 6. 1 2 __ V = ft 3 Multiply.

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**Finding Volume 10-8 Try This: Example 2B**

Course 1 10-8 Finding Volume Try This: Example 2B Find the volume of each triangular prism. B. 9 ft 5 ft 4.5 ft V = Bh Write the formula. V = ( • 4.5 • 9) • 5 1 2 __ B = • 4.5 • 9; h = 5. 1 2 __ V = ft3 Multiply.

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**Understand the Problem**

Course 1 10-8 Finding Volume 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.

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**Additional Example 3 Continued**

Course 1 10-8 Finding Volume 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.

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**Additional Example 3 Continued**

Course 1 10-8 Finding Volume Additional Example 3 Continued Solve 3 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 • 1 • 16, 1 • 2 • 8, 1 • 4 • 4, and 2 • 2 • 4 .

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**Additional Example 3 Continued**

Course 1 10-8 Finding Volume 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.

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**Understand the Problem**

Course 1 10-8 Finding Volume 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.

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**Try This: Example 3 Continued**

Course 1 10-8 Finding Volume 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.

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**Try This: Example 3 Continued**

Course 1 10-8 Finding Volume Try This: Example 3 Continued Solve 3 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 • 1 • 12, 1 • 2 • 6, 1 • 3 • 4, and 2 • 2 • 3.

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**Try This: Example 3 Continued**

Course 1 10-8 Finding Volume 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.

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**Insert Lesson Title Here**

Course 1 10-8 Finding Volume Insert Lesson Title Here Lesson Quiz Find the volume of each figure. 1. rectangular prism with length 20 cm, width 15 cm, and height 12 cm 2. triangular prism with a height of 12 cm and a triangular base with base length 7.3 cm and height 3.5 cm 3. Find the volume of the figure shown. 3,600 cm3 153.3 cm3 38.13 cm3

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