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Splash Screen

Splash Screen. Chapter 7. Lesson 7 - 6. (over Lesson 7-4). Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices. A B C D. cube ; 6 faces, all squares; 12 edges; 8 vertices B . cube; 4 faces, all squares; 12 edges; 8 vertices

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Splash Screen

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  1. Splash Screen Chapter 7 Lesson 7-6

  2. (over Lesson 7-4) Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices. • A • B • C • D cube; 6 faces, all squares; 12 edges; 8 vertices B.cube; 4 faces, all squares; 12 edges; 8 vertices C.cube; 4 faces, all squares; 8 edges; 12 vertices D.cube; 6 faces, all squares; 8 edges; 12 vertices

  3. (over Lesson 7-4) Identify the solid shown. Name the number and shapes of the faces. Then name the number of edges and vertices. • A • B • C • D A.rectangular prism; 4 faces, all rectangles; 12 edges; 8 vertices B.rectangular prism; 4 faces, all rectangles; 8 edges; 12 vertices C.rectangular prism; 6 faces, all rectangles; 12 edges; 8 vertices D.rectangular prism; 6 faces, all rectangles; 8 edges; 12 vertices

  4. (over Lesson 7-5) Find the volume of the given solid. Round to the nearest tenth if necessary. • A • B • C • D A.25.5 cm3 B.51 cm3 C.76.5 cm3 D.153 cm3

  5. (over Lesson 7-5) Find the volume of the given solid. Round to the nearest tenth if necessary. • A • B • C • D A.91.1 ft3 B.45.6 ft3 C.20.1 ft3 D.13.5 ft3

  6. Today’s lesson is about volume. For this lesson try drawing at least one 3-dimensional shape to help you better visualize the concept. Last week you were asked to reflect upon how you participated in each of the lessons and write a goal for the lesson of the day.

  7. Find the volumes of pyramids and cones. • cone

  8. Standard 7MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

  9. Prior Knowledge: V = 24in3 The volume of a rectangular prism with a base length of 4in, a width of 2in, & a height of 3in = 24in3. 3 in 2 in 4 in Something to Ponder: The volume of a rectangular pyramid with a base length of 4in, a width of 2in, & a height of 3in = 8in3. 3 in 4 in 2 in V = 8in3 New Knowledge: Let’s investigate! Is there a relationship between the volume of a prism & a pyramid?

  10. Compare the dimensions of each prism and pyramid & their volume. V = 96in3 V = 32in3 4 in 6 in 3 in 1 in 3 in 8 in 4 in 6 in V = 18in3 V = 6in3 8 in 1 in 3 in 3 in Is there a relationship between them?

  11. Find the Volume of a Pyramid The volume formula of a pyramid is: You must always begin a calculation such as this by 1st identifying the: _______________________________________________ Base of the Pyramid The base of this Pyramid is a: _______________________________________________ Rectangle

  12. Find the Volume of a Pyramid The volume of a pyramid is: Finding the volume of any 3-dimensional solid requires that you write the formula for the ________ of the base of the solid. area The base of this Pyramid is a rectangle. The formula for the area of a rectangle is: _______________________________________________ A = lwor A = 7cm3cm

  13. Find the Volume of a Pyramid The volume of a pyramid is: Now that we have the area of the base (21cm2) we have to multiply that times the ________ of the base of the pyramid. height The height of this Pyramid is 20cm. 21cm220cm = _______________________________________________ 420cm3

  14. Find the Volume of a Pyramid The volume of a pyramid is: Now that we have the area of the base multiplied times the area of the base, we need to ________ that by 3 to get our final answer. divide The volume of this Pyramid is 420cm3. 420cm2÷ 3 = _______________________________________________ 140cm3

  15. Find the Volume of a Pyramid Find the volume of the pyramid. Volume of a pyramid B = 7 ● 3, h = 20 Simplify. Answer: The volume is 140 cubic centimeters.

  16. Find the volume of the pyramid. • A • B • C • D A. 60 m3 B. 72 m3 C. 80 m3 D. 120 m3

  17. TOYS A company is designing pyramid shaped building blocks with a rectangular base. They want the volume of the blocks to be 18 cubic inches. If the length of the side of the base is 6inches and the width of the side of the base is 3 inches what should be the height of the blocks? • A • B • C • D 3 hin Start by plugging in data to the formula: V = ⅓ Bh 3 in 3 6 in 3 18 = ⅓ (6  3)h

  18. Now use the data and solve for h, the height. • A • B • C • D 18 = ⅓ (6  3)h 3 Xin 3in 3 6in 3

  19. TOYS A company is designing pyramid shaped building blocks with a rectangular base. They want the volume of the blocks to be 18 cubic inches. If the length of the side of the base is 6inches and the width of the side of the base is 3 inches what should be the height of the blocks? • A • B • C • D 3 Xin A. 6 in. B. 6.5 in. C. 3 in. D. 3.5 in. 3in 3 6in 3

  20. Prior Knowledge: The volume of a rectangular pyramid is ⅓ that of a rectangular prism with the same dimensions. 3 in V = 8in3 V = 8in3 V = 8in3 + + V = 24in3 = 2 in 4 in + + = 3 in 3 in 3 in 2 in 2 in 2 in 4 in 4 in 4 in Fact: - The formula for the volume of a rectangular prism is: V = Bh • The formula for the volume of a rectangular pyramid is: • V = ⅓Bh

  21. Reflective Knowledge: Considering the formula relationship between a rectangular prism (V= Bh) and a rectangular pyramid (V = ⅓Bh), do you think there is a similar relationship between a cylinder and a cone? r h

  22. New Knowledge: r h V = Bh or V = (πr2)h V = ⅓Bh or V = ⅓(πr2)h

  23. Find the Volume of a Cone Find the volume of the cone. Round to the nearest tenth. Volume of a cone Replace r with1.5 and h with 8. Simplify. Answer: The volume is about 18.8 cubic meters.

  24. Find the volume of the cone. Round to the nearest tenth. • A • B • C • D A. 28.5 in3 B. 29.2 in3 C. 34.1 in3 D. 37.7 in3

  25. Reflect upon the lesson today. Ask yourself: “Did I make a connection between what I had learned previously with what I was taught today? Do I ever think about prior lessons and how they can help me with new lessons. Write down how often you make a reflect back on a previous lesson you’ve had and how it has helped you make a connection with a new concept.

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