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Unit 7: Solid Figures and Measurement

Unit 7: Solid Figures and Measurement. Now’s the time to SHAPE UP!!. Warm-Ups

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Unit 7: Solid Figures and Measurement

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  1. Unit 7: Solid Figures and Measurement Now’s the time to SHAPE UP!!

  2. Warm-Ups Jim-Bob went to visit Ellie Mae at the pet store where she worked. Her boss had asked her to divide 36 goldfish, 42 guppies, and 126 white fish equally into as many aquariums as possible. What is the greatest number of aquariums she can fill?

  3. Volume What am I Learning Today? How will I show that I learned it? Determine the formula for finding the volume of fundamental solid figures Compute volume using formulas and appropriate units of measure Solve application problems involving volume

  4. Vocabulary • Volume: The number of cubic units needed to fill a given space. What exactly does this mean? It takes 10 centimeter cubes to cover the bottom layer of this rectangular prism (5cm x 2cm). It will take 3 layers of 10 cubes each to fill the prism. It takes 30 cubes or (5cm · 2cm · 3cm). Volume is expressed in cubic units, so the volume of the prism is 5 cm · 2 cm · 3 cm = 30 cm3.

  5. Volume of a Rectangular Prism V = Bh h Volume Height Base Area Base Area What is the shape of the base here? What is the formula for its area? (Remember the “Base Area” formula will be determined by the base shape.) B = l x w

  6. Find the volume of the rectangular prism. 16 in. 12 in. 29 in. V = Bh or V = lx w x h Write the formula. Substitute the values. l = 29w = 12h = 16 V = 29•12•16 V = 348 •16 Multiply and label correctly. V = 5,568 in3

  7. Practice Volume of cubes and rectangular prisms: http://www.thatquiz.org/tq-4/?-j20k0-la-n35-p0 Volume and Surface Area mixed: http://www.thatquiz.org/tq-4/?-j24u0-la-n35-p0

  8. Questions Notes Questions Answers How do I find the volume for any prism or cylinder? Use the formula V= Bh, where B is the area of the base, and h is the height. 2 m V =Bhorl x wx h What is the formula for the volume of a rectangular prism ? V=Bhorl x wx h V= 6 x 5 or 3 x 2 x 5 V= 30 m3 5 m 3 m What is the volume of a cylinder? V =Bh orTTr2h 2 cm V =BhorTTr2h V = 3.14 x 22 x 4 V = 6.28 x 4 x 4 V = 25.12 x 4 = 100.48 cm3 4 cm

  9. Volume of a Cylinder Radius V = Bh Base Area Base Area h Height Volume B = r2 Base Area Radius

  10. Multiply and label correctly. V 565.2 ft3 Replace  with 3.14, r with 6, and h with 5. V 3.14  62 5 V 3.14  36  5 V 3.14  180 Find the volume of the cylinder to the nearest cubic unit. 6 ft 5 ft V = Bh or r2h Write the formula.

  11. Finding the Volume of a Cylinder 5 cm Find the volume of a cylinder with height 10 cm and radius 5cm. V = Bh 10 cm V = Bh

  12. Cylinder 2 has the greater volume because 169.56 cm3 > 84.78 cm3. V 3.14  (1.5)2 12 V = r2h V 84.78 cm3 V 3.14  32 6 V =r2h V 169.56 cm3 Find which cylinder has the greater volume. Cylinder 1: Cylinder 2:

  13. V =3,600 cm3 V = 192.92 ft3 Now Try This!! Find the volume of each figure. 1) Rectangular prism with length of 20 cm, width of 15 cm, and height of 12 cm. 2) Cylinder with radius = 3.2 ft, height = 6 ft

  14. Practice Volume of Cylinders: http://www.thatquiz.org/tq-4/?-j2800-la-n35-p0 Volume and Surface Area mixed: http://www.thatquiz.org/tq-4/?-j2cu0-la-n35-p0

  15. Questions Notes Questions Answers V = 1/3Bhor1/3 (l x wx h) What is the formula for the volume of a pyramid ? V= 1/3Bh or 1/3 (l x wx h) V= 1/3 (8 x 3) or 1/3 (4 x 2 x 3) V= 1/3 (24) V = 8 cm3 3 cm 4 cm 2 cm What is the volume of a cone? V = 1/3Bh or 1/3 (TTr2h) V = 1/3Bhor 1/3 (TTr2h) V = 1/3 (3.14 x 22 x 4) V = 1/3 (3.14 x 4 x 4) V = 1/3 (12.56 x 4) V = 1/3 (50.24) V = 16.746 cm3 4 cm 2 cm

  16. Volume of a Pyramid V = ⅓Bh h Base Area Height Volume What is the shape of the base here? What is the formula for its area? (Remember the “Base Area” formula will be determined by the base shape.) Base Area B = l x w What do you notice about the relationship between the volume of a pyramid and a prism?

  17. Find the volume of the pyramid. V = 1/3Bhor1/3 (l x wx h) V = 1/3 (14 • 10 • 19) V = 1/3 (140 • 19) V = 1/3 (2660) V = 886.67 cm3

  18. Volume of a Cone V = ⅓Bh Height Volume Base Area h B = r2 r Radius Base Area What do you notice about the relationship between the volume of a cone and a cylinder?

  19. V 1/3 (3.14  42 16) V 1/3 (3.14  16  16) V 1/3 (50.24  16) V 1/3 (803.84) V 267.95 cm3 Find the volume of the cone. V = 1/3Bh or 1/3 (TTr2h)

  20. Finding the Volume of a Cone The radius of the base of a cone is 6 m. Its height is 13 m. Find the volume. V = ⅓Bh V = ⅓Bh

  21. V = 25.12 in3 V =6.67 m3 Now Try This!! Find the volume of each figure. 1) Pyramid with a height of 4 m, a length of 2.5 m and width of 2 m. 2) Cone with diameter = 4 in, height = 6 in

  22. Practice Volume of Cones: http://www.thatquiz.org/tq-4/?-j3000-la-n35-p0 Volume and Surface Area mixed: http://www.thatquiz.org/tq-4/?-j3cu1-la-n35-p0

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