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Surface area and volume of cuboids

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Surface area and volume of cuboids

  1. 1. Shape and Space Cuboids
  2. 2. Surface area of a cuboidTo find the surface area of a shape, we calculate thetotal area of all of the faces. A cuboid has 6 faces. The top and the bottom of the cuboid have the same area.
  3. 3. Surface area of a cuboidTo find the surface area of a shape, we calculate thetotal area of all of the faces. A cuboid has 6 faces. The front and the back of the cuboid have the same area.
  4. 4. Surface area of a cuboidTo find the surface area of a shape, we calculate thetotal area of all of the faces. A cuboid has 6 faces. The left hand side and the right hand side of the cuboid have the same area.
  5. 5. 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 5 cm 8 cm surface area of this cuboid? 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
  6. 6. 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
  7. 7. Formula for the surface area of a cuboidWe can find the formula for the surface area of a cuboidas follows. Surface area of a cuboid = w l 2 × lw Top and bottom h + 2 × hw Front and back + 2 × lh Left and right side = 2lw + 2hw + 2lh
  8. 8. 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
  9. 9. Chequered cuboid problemThis cuboid is made from alternate purple and greencentimetre 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
  10. 10. Surface area of a prism What is the surface area of this L-shaped prism? 3 cm To find the surface area of 3 cm this shape we need to add together the area of the two 4 cm L-shapes and the area of the 6 rectangles that make up6 cm the surface of the shape. Total surface area = 2 × 22 + 18 + 9 + 12 + 6 + 6 + 15 5 cm = 110 cm2
  11. 11. 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 3 cm 18 cm2 3 cm 6 cm face. Then add the5 cm 15 cm2 30 cm2 15 cm2 30 cm2 areas together to find the surface area. 3 cm 18 cm2 3 cm Surface Area = 126 cm2
  12. 12. Making cuboidsThe following cuboid is made out of interlocking cubes. How many cubes does it contain?
  13. 13. 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
  14. 14. Making cuboidsThe amount of space that a three-dimensional object takesup is called its volume.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, widthand height.Liquid volume or capacity is measured in ml, l, pints orgallons.
  15. 15. 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
  16. 16. 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
  17. 17. Volume and displacement
  18. 18. 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 cm 3 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 cm 3.
  19. 19. Volume of a prism made from cuboids What is the volume of this L-shaped prism? 3 cm 3 cm We can think of the shape as two 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
  20. 20. Volume of a prismRemember, a prism is a 3-D shape with the samecross-section throughout 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
  21. 21. 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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