Soumya1

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Soumya1

  1. 1. CubeA Are all the faces the same? YES4m How many faces are there? 6 Find the Surface area of one of the faces. 4 x 4 = 16 Take that times the number of faces. X6 96 m2 SA for a cube.
  2. 2. Surface Area What does it mean to you? Does it have anything to do with what is in the inside of the prism.? Surface area is found by finding the area of all the sides and then adding those answers up. How will the answer be labeled? Units2 because it is area!
  3. 3. Triangular Prism How many faces are4 5 there? 5 How many of each shape does it take to make this prism? 10 m 3 2 triangles and 3 rectangles = SA of a triangular prism Find the surface area. Start by finding the area of the triangle. 4 x 3/2 = 6 x 2= 12 How many triangles were there? 5 x 10 = 50 = front 2 4 x 10 = 40 = back Find the area of the 3 3 x 10 = 30 = bottom rectangles. What is the final SA? SA = 132 m2
  4. 4. SA You can find the SA of any prism by using the basic formula for SA which is 2B + LSA= SA LSA= lateral Surface area LSA= perimeter of the base x height of the prism B = the base of the prism.
  5. 5. Triangular Prisms Use the same triangular prism we used before. Let’s us the formula this time. 2B + LSA=SA Find the area of the base, which is a triangle because it is a triangular prism. You will need two of them. Now, find the perimeter of that same base and multiply it by how many layer of triangles are in the picture. That is the LSA. Add that to the two bases. Now you should have the same answer as before. Either way is the correct way.
  6. 6. Cylinders What does it take to make this? 6 10m 2 circles and 1 rectangle= a cylinder 2B + LSA = SA 2B 3.14 x 9 = 28.26 X 2 = 56.52+ LSA(p x H) 3.14 x 6 =18.84 x 10 = 188.4 SA = 244.9 2
  7. 7.  Why should you learn about surface area? Is it something that you will ever use in everyday life? If so, who do you know that uses it? Have you ever had to use it outside of math?
  8. 8. Surface Area Triangular prism – a prism with two parallel, equal triangles on opposite sides. To find the surface area of a triangularh w prism we can add l up the areas of the separate faces.
  9. 9. Surface Area  In a triangular prism there are two pairs of opposite and equal triangles. We can find the surface area of this prism by adding the areas of the pink 8 cm side (A), the orange sides (B), the green A bottom (C) and the two ends (D).2 cm B C 5 cm 7 cm
  10. 10. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A2 cm B C 5 cm B 7 cm C D Total
  11. 11. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A 40 cm2 1 40 cm22 cm B C 5 cm B 7 cm C D Total
  12. 12. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A 40 cm2 1 40 cm22 cm B C 5 cm B 10 cm2 1 10 cm2 7 cm C D Total
  13. 13. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A 40 cm2 1 40 cm22 cm B C 5 cm B 10 cm2 1 10 cm2 7 cm C 35 cm2 1 35 cm2 D Total
  14. 14. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A 40 cm2 1 40 cm22 cm B C D 5 cm B 10 cm2 1 10 cm2 7 cm C 35 cm2 1 35 cm2 D 7 cm2 2 14 cm2 Total
  15. 15. Surface Area  We should use a table to tabulate the various areas. Example: Side Area Number Total of Sides Area 8 cm A A 40 cm2 1 40 cm22 cm B C D 5 cm B 10 cm2 1 10 cm2 7 cm C 35 cm2 1 35 cm2 D 7 cm2 2 14 cm2 Total 5 99 cm2
  16. 16. Example: Surface Area Now you try...find the surface area! B Side Area No of Area Sides C
  17. 17. Example: Surface Area Now you try...find the surface area! B Side Area No of Area Sides 2.1m C 2.0m 11.0m2.0m
  18. 18. Shape and Space Cuboids
  19. 19. Surface area of a cuboidTo find the surface area of a shape, we calculate the total area of all of thefaces. A cuboid has 6 faces. The top and the bottom of the cuboid have the same area.
  20. 20. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The front and the back of the cuboid have the same area.
  21. 21. Surface area of a cuboidTo find the surface area of a shape, we calculate the total area of all of thefaces. A cuboid has 6 faces. The left hand side and the right hand side of the cuboid have the same area.
  22. 22. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. Can you work out the surface area of 5 cm this cuboid? 8 cm The area of the top = 8 × 5 = 40 cm27 cm The area of the front = 7 × 5 = 35 cm2 The area of the side = 7 × 8 = 56 cm2
  23. 23. Surface area of a cuboid To find the surface area of a shape, we calculate the total area of all of the faces. 5 cm So the total surface area = 8 cm 2 × 40 cm2 Top and bottom7 cm + 2 × 35 cm2 Front and back + 2 × 56 cm2 Left and right side = 80 + 70 + 112 = 262 cm2
  24. 24. Formula for the surface area of a cuboidWe can find the formula for the surface area of a cuboid as follows. Surface area of a cuboid = w l 2 × lw Top and bottom + 2 × hw Front and back h + 2 × lh Left and right side = 2lw + 2hw + 2lh
  25. 25. Surface area of a cube How can we find the surface area of a cube of length x? All six faces of a cube have the same area. The area of each face is x × x = x2 Therefore, x Surface area of a cube = 6x2
  26. 26. Chequered cuboid problemThis cuboid is made from alternate purple and green centimetre cubes. What is its surface area? Surface area =2×3×4+2×3×5+2×4×5 = 24 + 30 + 40 = 94 cm2 How much of the surface area is green? 48 cm2
  27. 27. Surface area of a prism What is the surface area of this L-shaped prism? 3 cm To find the surface area of this shape 3 cm we need to add together the area of the two L-shapes and the area of the 6 rectangles that make up the surface of 4 cm the shape.6 cm Total surface area = 2 × 22 + 18 + 9 + 12 + 6 + 6 + 15 5 cm = 110 cm2
  28. 28. Using nets to find surface area It can be helpful to use the net of a 3-D shape to calculate its surface area. Here is the net of a 3 cm by 5 cm by 6 cm cuboid 6 cm Write down the area of each face. 3 cm 18 cm2 3 cm 6 cm Then add the areas together to find the5 cm 15 cm2 30 cm2 15 cm2 30 cm2 surface area. 3 cm 18 cm2 3 cm Surface Area = 126 cm2
  29. 29. Making cuboidsThe following cuboid is made out of interlocking cubes. How many cubes does it contain?
  30. 30. Making cuboidsWe can work this out by dividing the cuboid into layers. The number of cubes in each layer can be found by multiplying the number of cubes along the length by the number of cubes along the width. 3 × 4 = 12 cubes in each layer There are three layers altogether so the total number of cubes in the cuboid = 3 × 12 = 36 cubes
  31. 31. Making cuboidsThe amount of space that a three-dimensional object takes up is called itsvolume.Volume is measured in cubic units.For example, we can use mm3, cm3, m3 or km3.The 3 tells us that there are three dimensions, length, width and height.Liquid volume or capacity is measured in ml, l, pints or gallons.
  32. 32. Volume of a cuboid We can find the volume of a cuboid by multiplying the area of the base by the height. The area of the base = length × width So,height, h Volume of a cuboid = length × width × height = lwh length, l width, w
  33. 33. Volume of a cuboid What is the volume of this cuboid? Volume of cuboid = length × width × height 5 cm = 5 × 8 × 13 8 cm 13 cm = 520 cm3
  34. 34. Volume and displacement
  35. 35. Volume and displacement By dropping cubes and cuboids into a measuring cylinder half filled with water we can see the connection between the volume of the shape and the volume of the water displaced. 1 ml of water has a volume of 1 cm3 For example, if an object is dropped into a measuring cylinder and displaces 5 ml of water then the volume of the object is 5 cm3. What is the volume of 1 litre of water? 1 litre of water has a volume of 1000 cm3.
  36. 36. Volume of a prism made from cuboids What is the volume of this L-shaped prism? 3 cm We can think of the shape as two 3 cm cuboids joined together. 4 cm Volume of the green cuboid = 6 × 3 × 3 = 54 cm36 cm Volume of the blue cuboid = 3 × 2 × 2 = 12 cm3 Total volume 5 cm = 54 + 12 = 66 cm3
  37. 37. Volume of a prismRemember, a prism is a 3-D shape with the same cross-sectionthroughout its length. 3 cm We can think of this prism as lots of L- shaped surfaces running along the length of the shape. Volume of a prism = area of cross-section × length If the cross-section has an area of 22 cm2 and the length is 3 cm, Volume of L-shaped prism = 22 × 3 = 66 cm3
  38. 38. Volume of a prism What is the volume of this prism? 12 m 4m 7m 3m 5m Area of cross-section = 7 × 12 – 4 × 3 = 84 – 12 = 72 m2 Volume of prism = 5 × 72 = 360 m3

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