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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 5-5c. Objective. Find the volumes of prisms and cylinders. Prism Volume = Area of base  height of figure. Cylinder Volume. Example 5-5c. Vocabulary. Volume.

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  1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 5-5c Objective Find the volumes of prisms and cylinders Prism Volume = Area of base  height of figure Cylinder Volume

  4. Example 5-5c Vocabulary Volume The number of cubic units needed to fill the space occupied by a solid

  5. Example 5-5c Vocabulary Cylinder A solid whose bases are congruent, parallel circles, connected with a curved side

  6. Example 5-5c Vocabulary Complex solid An object made up of more than one type of solid

  7. Lesson 5 Contents Example 1Find the Volume of a Rectangular Prism Example 2Find the Volume of a Triangular Prism Example 3Find the Volumes of Cylinders Example 4Find the Volumes of Cylinders Example 5Find the Volume of a Complex Solid

  8. Example 5-1a Find the volume of the prism. Volume = Area of base  Height of prism V = (L  W) Height of prism The prism has a rectangular base Remember: The top and base have the same dimensions on a prism Replace formula for rectangle in “area of base” Note: Area of base is in parenthesis because area must be figured first 1/5

  9. Example 5-1a Find the volume of the prism. Volume = Area of base  Height of prism V = (L  W) Height of prism  5 in)  11 in V = (7 in Replace L with 7 in Replace W with 5 in Replace Height of prism with 11 in Follow order of operations P E MD AS Work inside parenthesis 1/5

  10. Example 5-1a Find the volume of the prism. Volume = Area of base  Height of prism V = (L  W) Height of prism  5 in)  11 in V = (7 in Multiply 7 in  5 in V = 35 in2 11 in Multiply 35 in2 5 in V = 385 in3 Answer: 1/5

  11. Example 5-1b Find the volume of the prism. Answer: V = 120 in3 1/5

  12. Example 5-2a Find the volume of the prism. Volume = Area of base  Height of prism Volume = ( bh)  Height of prism The prism has a triangular base Note: The base does not have to be on the bottom Replace formula for triangle in “area of base” 2/5

  13. Example 5-2a Find the volume of the prism. Volume = Area of base  Height of prism Volume = ( bh)  Height of prism  4 ft  9 ft) Volume = (  15 ft Replace b with base of triangle which is 15 ft Replace h with height of triangle which is 9 ft Replace height of prism with 4 ft 2/5

  14. Example 5-2a Find the volume of the prism. Volume = Area of base  Height of prism Volume = ( bh)  Height of prism Follow order of operations P E MD AS  4 ft  9 ft) Volume = (  15 ft Work inside parenthesis Volume = 67.5 ft2 4 ft Multiply  15 ft  9 ft Volume = 270 ft3 Answer: Multiply 67.5 ft2 4 ft 2/5

  15. Example 5-2b Find the volume of the prism. Answer: V = 45 ft3 2/5

  16. Example 5-3a Find the volume of the cylinder. Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [3 cm]2) The prism has a circle base Replace formula for circle in “area of base” Replace r with 3 cm Note: Put 3 cm in enclosures because must square both number and unit of measure 3/5

  17. Example 5-3a Find the volume of the cylinder. Volume = Area of base  Height of prism Volume = (  r2)  Height of prism  12 cm Volume = (  [3 cm]2) Replace height of prism with 12 cm Follow order of operations P E MD AS Work inside parenthesis that are inside the parenthesis! 3/5

  18. Example 5-3a Find the volume of the cylinder. Volume = Area of base  Height of prism Volume = (  r2)  Height of prism  12 cm Volume = (  [3 cm]2) Volume = (  9 cm2)  12 cm Multiply 3 cm  3 cm Volume = 28.26 cm2  12 cm Multiply  9 cm2 Do not clear display on calculator Volume = 339.29 cm3 Answer: Multiply 28.26 cm2  12 cm 3/5

  19. Example 5-3b Find the volume of the cylinder. Answer: V = 169.56 in3 3/5

  20. Example 5-4a Find the volume of the cylinder. diameter of base,18 yd; height, 25.4 yd Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [9 yd]2) A cylinder has a circle base Replace formula for circle in “area of base” Replace r with 9 yd Remember: radius is half the diameter 4/5

  21. Example 5-4a Find the volume of the cylinder. diameter of base,18 yd; height, 25.4 yd Volume = Area of base  Height of prism Volume = (  r2)  Height of prism  25.4 yd Volume = (  [9 yd]2) Replace height of prism with 25.4 yd Follow order of operations P E MD AS Work inside parenthesis that are inside the parenthesis! 4/5

  22. Example 5-4a Find the volume of the cylinder. diameter of base,18 yd; height, 25.4 yd Volume = Area of base  Height of prism Volume = (  r2)  Height of prism  25.4 yd Multiply 9 yd  9 yd Volume = (  [9 yd]2) Multiply  81 yd2 Volume = (  81 yd2)  25.4 yd Do not clear display on calculator Volume = 254.34 yd2  25.4 yd Answer: Volume = 6,460.24 yd3 Multiply 254.34 yd2  25.4 yd 4/5

  23. Example 5-4b Find the volume of the cylinder. diameter of base, 8 yd; height, 10 yd Answer: V = 502.40 yd3 4/5

  24. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. The big shape is a rectangular prism The hole in the box is a cylinder Identify each shape Find the area of each shape and subtract the cylinder from the rectangular prism 5/5

  25. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Rectangular Prism: Volume = Area of base  Height of prism V = (L  W) Height of prism V = (4 cm  3 cm) Replace formula for circle in “area of base” Replace L with 4 cm Replace W with 3 cm 5/5

  26. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Rectangular Prism: Volume = Area of base  Height of prism V = (L  W) Height of prism V = (4 cm  3 cm)  6 cm Replace height of prism with 6 cm Follow order of operations P E MD AS Work inside parenthesis 5/5

  27. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Rectangular Prism: Volume = Area of base  Height of prism V = (L  W) Height of prism V = (4 cm  3 cm)  6 cm Multiply 4 cm  3 cm V = 12 cm2 6 cm Multiply 12 cm2 6 cm V = 72 in3 5/5

  28. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Cylinder: Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [1 cm]2)  3 cm Replace formula for circle in “area of base” Replace r with 1 cm Replace height of prism with 3 cm 5/5

  29. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Cylinder: Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [1 cm]2)  3 cm Follow order of operations P E MD AS Work inside parenthesis that are inside the parenthesis! 5/5

  30. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Cylinder: Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [1 cm]2)  3 cm Multiply 1 cm  1 cm Volume = (  1 cm2)  3 cm Multiply  1 cm2 Volume = 3.14 cm2  3 cm Do not clear display on calculator 5/5

  31. Example 5-5a TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. Cylinder: Volume = Area of base  Height of prism Volume = (  r2)  Height of prism Volume = (  [1 cm]2)  3 cm Multiply 3.14 cm2  3 cm Volume = (  1 cm2)  3 cm Volume = 3.14 cm2  3 cm Volume = 9.42 cm3 5/5

  32. Example 5-5b Rectangular Prism Cylinder V = 72 in3 V = 9.42 cm3 Subtract the volume of cylinder from volume of prism V = 72 in3 - 9.42 cm3 Answer: V = 62.58 cm3 5/5

  33. Example 5-5c * HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled? Answer: 5/5

  34. End of Lesson 5 Assignment

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