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Volumes of prisms and surface areas

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- 1. Volumes and surface area<br />BTEOTSSBAT solve problems involving volume and surface area<br />
- 2. Key words<br />volume<br />cross section<br />prism<br />cube<br />cuboid<br />cylinder<br />
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. A square prism is called a cube<br />
- 15. A square prism is called a cube<br />A rectangular prism is called a cuboid<br />
- 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. 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. 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. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 20. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 21. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 22. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 23. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 24. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 25. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 26. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 27. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 28. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 29. Example<br />Find the surface area of the cuboid which is 4 cm 5 cm 10 cm<br />
- 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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