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Volume Surface Area (3).pptx
- 2. Discuss… What’s the same and what’s different??
- 3. The volume of a solid is the amount of space occupied by the solid. The greater the volume of a solid the more space it takes up. The volume of a solid is the number of unit cubes that the solid can be divided into. 1 unit 1 unit 1 unit 2 units 3 units 4 units 24 unit cubes altogether
- 4. This cuboid is made up of centimetre cubes (cm³). What is its volume? 12 cm³
- 5. 5 cm 10 cm 2 cm What is the volume of this cuboid? 100 cm³
- 6. 6 m 3 m 2 m What is the volume of this cuboid? 36 m³
- 7. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 8. Answers 1)5 x 2 x 7 = 70 cm3 2)3 x 2 x 8 = 48 cm3 3)5 x 6 x 2 = 60 cm3 4)2 x 2 x 6 = 24 cm3 5)5 x 2 x 3 = 30 cm3 6)2 x 7 x 4 = 56 cm3 7)7 x 7 x 2 = 98 cm3 8)2 x 4 x 5 = 40 cm3 9)2 x 9 x 2 = 36 cm3 Extension question: 54 ÷ (9 x 2) = 54 ÷ 18 = 3cm
- 9. Josh is having a birthday party! He wants to make boxes of sweets to give to his guests. He starts with a square piece of paper that measures 20cm x 20cm. How big should the squares be that he cuts out of the corners to maximise the volume of the box?
- 10. Record your results in the table provided. Don’t forget your units of measurements!
- 11. Extension questions 1. What if the square you cut out doesn’t have to use whole number measurements (e.g. 2.4cm)? Would this change your answer? 2. What if you started from a 10cm x 20cm rectangle instead? What would the biggest volume be?
- 12. Surface areas of cubes and cuboids What is surface area? Think about finding the area of a square or rectangle… width height Area = height x width What about if we phrase surface area differently… The area of the surface
- 13. The area of the surface How could we find the surface area of a cuboid using the height, width and length? H L W How many faces does a cuboid have? 6 So we could add together the areas of all 6 faces! Surface areas of cubes and cuboids
- 14. H L W Surface area = (Length x Height) + (Length x Height) + (Height x Width) + (Height x Width) + (Length x Width) + (Length x Width) Front Back Left Right Top Bottom Top Right Front Left Bottom Back By adding the area of all of the faces, we can find the surface area of the whole cuboid.
- 15. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 17. A cube is cut out of a larger cube and stuck into the corner, as shown. What is the surface area of the resulting shape? All lengths are in centimetres
- 18. HINT: There are 15 faces!
- 19. Total Surface Area = 115cm²
- 20. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 21. Starter Calculate the areas of the following shapes 4cm 4cm 3cm 5cm 5cm 6cm 3cm
- 22. Starter Calculate the areas of the following shapes 4cm 4cm 3cm 5cm 5cm 6cm 3cm 16cm² 15cm² 15cm² 28.26cm²
- 23. Cross Section – The shape of the slice Prism – A shape that has the same cross section all the way through
- 24. Cuboid Triangular prism Pentagonal prism A prism is a 3-D shape which has the same cross-section throughout its height.
- 26. Volume of a prism = area of cross-section x vertical height Cross-section Vertical height
- 27. Example: Find the volume of this prism 25 cm2 7 cm Volume of a prism = area of cross-section x vertical height 25 x 7 = 175 cm³
- 28. Example: Find the volume of this prism 3 cm 6 cm 10 cm Volume of a prism = area of cross-section x vertical height Area of cross-section = ½ x 6 x 3 Volume = 9 x 10 cm² = 9 = 90 cm³
- 30. Thoughts and crosses Calculate the volumes of 4 of the prisms, either vertically, horizontally or diagonally Volume of Prisms
- 31. The area of the surface How could we find the surface area of a triangular prism using the height, width, depth and slant height? How many faces does a triangular prism have? 5 So we could add together the areas of all 5 faces! H D W S
- 32. Surface area = (Width x Height ÷ 2) + (Width x Height ÷ 2) + (Height x Depth) + (Slant x Depth) + (Width x Depth) Front Back Left Right Bottom By adding the area of all of the faces, we can find the surface area of the whole triangular prism. H D W S Right Front Left Bottom Back
- 33. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 35. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 36. Starter Calculate the areas and circumferences of these circles to 1 d.p. Q1 Q2 Q3 Q6 Q4 Q5 7 cm 4.5 cm 8 cm 3 cm 2.5 cm 2 cm
- 37. Answers Q1 A = 38.5 cm², C = 22.0 cm Q2 A = 19.6 cm², C = 15.7 cm Q3 A = 50.3 cm², C = 25.1 cm Q4 A = 12.6 cm², C = 12.6 cm Q5 A = 28.3 cm², C = 18.8 cm Q6 A = 15.9 cm², C = 14.1 cm
- 38. Calculate the volume of this cylinder. Give your answer to 3 s.f. Volume of a prism = area of cross section x length Area of cross-section = π x 12² = 452.389… cm² Volume = 452.389… x 20 = 9047.8 cm³ Area of cross-section = π x 5² = 78.539… cm² Volume = 78.539… x 12 = 943 cm³ Calculate the volume of this cylinder. Give your answer to 1 d.p.
- 39. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 41. Circumference = πd Height (h) πd h Surface area of curved part of cylinder = πdh
- 42. Surface area of curved part of cylinder = πdh Area of top circle = πr² Area of bottom circle = πr² Surface area of cylinder = 2πr² + πdh
- 43. 4cm 6cm Calculate the total surface area of the cylinder, giving your answer to 1 d.p.: Top = π x 2² = 12.566… cm² Curved = π x 4 x 6 = 75.398… cm² Bottom = π x 2² = 12.566… cm² Total = 12.566… + 75.398… + 12.566… = 100.5 cm²
- 44. How confident do you feel with this topic? Write red, amber or green in your book! Complete the corresponding activity
- 45. 192 cm² 10995.6 cm²
- 47. Your friend has missed today’s lesson. Write a text (in your book!) telling them what they need to know. Plenary