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Understanding Volume Calculations for Prisms and Cylinders

This instructional guide covers the concepts of volume calculation for various three-dimensional shapes, specifically prisms and cylinders. It includes clear formulas, step-by-step examples, and vocabulary definitions. You'll learn how to find the volume of rectangular prisms, triangular prisms, cylinders, and complex solids, with the equations being broken down for ease of understanding. Key terms such as volume, prism, cylinder, and base area are defined for better comprehension of the material. Perfect for students looking to strengthen their geometry skills!

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Understanding Volume Calculations for Prisms and Cylinders

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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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