Volumes And Surface Area

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Volumes of prisms and surface areas

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Volumes And Surface Area

  1. 1. Volumes and surface area<br />BTEOTSSBAT solve problems involving volume and surface area<br />
  2. 2. Key words<br />volume<br />cross section<br />prism<br />cube<br />cuboid<br />cylinder<br />
  3. 3. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />
  4. 4. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />
  5. 5. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br />
  6. 6. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br />x 100<br />
  7. 7. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />
  8. 8. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />x 100<br />
  9. 9. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />x 100<br /> = 5000 cm x cm x m<br />
  10. 10. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />x 100<br /> = 5000 cm x cm x m<br />x 100<br />
  11. 11. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />x 100<br /> = 5000 cm x cm x m<br />x 100<br />= 500 000 cm x cm x cm = cm³<br />
  12. 12. Volume is the amount of space a solid object takes up. <br />The units are mm³, cm³, m³, km³ and so on<br />Convert m³ into cm³<br />A box has a volume of 0.5 m³.<br />It needs to fit into a bag of size 100 000 cm³. Will it fit?<br />0.5 m³ = 0.5 m x m x m<br /> = 50 cm x m x m<br />x 100<br />x 100<br /> = 5000 cm x cm x m<br />So, no it won’t fit!<br />x 100<br />= 500 000 cm x cm x cm = cm³<br />
  13. 13. Prisms<br />Shapes that have a uniform cross section (ie all the same all the way through) are called prisms.<br />The volume of a prism is the cross-sectional area  length.<br />
  14. 14. A square prism is called a cube<br />
  15. 15. A square prism is called a cube<br />A rectangular prism is called a cuboid<br />
  16. 16. A square prism is called a cube<br />A rectangular prism is called a cuboid<br />A circular prism is called a cylinder<br />
  17. 17. Now try these<br />Find the volume of the following cuboids<br /> 4 cm<br />2 cm high 3 cm wide 2 cm<br /> 5 cm 3 cm<br />2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the volume of the disk.<br />3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the volume of the tin.<br />
  18. 18. Surface area<br />All 3D shapes have a surface area.<br />The surface area is the sum of the area of all the sides of a shape.<br />The surface area of a cuboid is the sum of all the 6 rectangular faces.<br />The rectangular faces can be grouped in pairs.<br />
  19. 19. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  20. 20. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  21. 21. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  22. 22. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  23. 23. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  24. 24. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  25. 25. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  26. 26. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  27. 27. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  28. 28. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  29. 29. Example<br />Find the surface area of the cuboid which is 4 cm  5 cm  10 cm<br />
  30. 30. Now try these<br />Find the surface areaof the following cuboids<br /> 4 cm<br />2 cm high 3 cm wide 2 cm<br /> 5 cm 3 cm<br />2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the surface areaof the disk.<br />3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the surfaceof the tin.<br />

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