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Warm up #3 Page 11 draw and label the shape

Warm up #3 Page 11 draw and label the shape. 1 . The area of a rectangular rug is 40 yd 2 . If the width of the rug is 10 yd , what is the length of the rug? 2 . The perimeter of a square rug is 16yd . If the width of the rug is 4 yd , what is the length of the rug?

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Warm up #3 Page 11 draw and label the shape

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  1. Warmup #3 Page 11drawand labeltheshape 1. The area of a rectangular rug is 40 yd2. If the width of the rug is 10 yd, what is the length of the rug? 2. The perimeter of a square rug is 16yd. If the width of the rug is 4 yd, what is the length of the rug? 3. Jose wants new carpeting for his living room. His living room is an 9 m by 9 m rectangle. How much carpeting does he need to buy to cover his entire living room? 4. Patricia has a rectangular flower garden that is 10 ft long and 5 ft wide. One bag of soil can cover 10 ft2. How many bags will she need to cover the entire garden?

  2. A Prism Cylinder Cuboid Cross section Triangular Prism Trapezoid Prism Volume of Prism = length xCross-sectional area

  3. h r b Area Rectangle = Base x height Area Circle = πr2 a h h b Area Trapezium = ½ x (a + b) x h b Area Triangle = ½ x Base x height Area Formulae

  4. Geometry Surface Area of Triangular and cuboid Prisms

  5. Surface Area • Triangular prism – a prism with two parallel, equal triangles on opposite sides. To find the surface area of a triangular prism we can add up the areas of the separate faces. h w l

  6. 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 side (A), the orange sides (B), the green bottom (C) and the two ends (D). 8 cm A 2 cm B 5 cm C 7 cm

  7. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm C 7 cm

  8. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm C 7 cm

  9. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm C 7 cm

  10. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm C 7 cm

  11. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm D C 7 cm

  12. Surface Area • We should use a table to tabulate the various areas. Example: 8 cm A 2 cm B 5 cm D C 7 cm

  13. Surface Area Example: B • Now you try...find the surface area! 2m C 2m 11m 2m

  14. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. A cuboid has 6 faces. The top and the bottom of the cuboid have the same area.

  15. Surface area of a cuboid To find the surfacearea 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.

  16. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total 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.

  17. Formula for the surface area of a cuboid w l 2 × lw Top and bottom Front and back + 2 × hw h + 2 × lh Left and right side We can find the formula for the surface area of a cuboid as follows. Surface area of a cuboid = = 2lw + 2hw + 2lh

  18. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. Can you work out the surface area of this cuboid? 5 cm 8 cm The area of the top = 8 × 5 = 40 cm2 7 cm The area of the front = 7 × 5 = 35 cm2 The area of the side = 7 × 8 = 56 cm2

  19. Surface area of a cuboid To find the surfacearea of a shape, we calculate the total area of all of the faces. So the total surface area = 5 cm 8 cm 2 × 40 cm2 Top and bottom 7 cm + 2 × 35 cm2 Front and back + 2 × 56 cm2 Left and right side = 80 + 70 + 112 = 262 cm2

  20. Chequered cuboid problem This 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

  21. 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 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 the shape. 3 cm 4 cm 6 cm Total surface area = 2 × 22 + 18 + 9 + 12 + 6 + 6 + 15 5 cm = 110 cm2

  22. Using nets to find surface area 6 cm 3 cm 3 cm 6 cm 5 cm 3 cm 3 cm Here is the net of a 3 cm by 5 cm by 6 cm cuboid Write down the area of each face. Then add the areas together to find the surface area. 18 cm2 15 cm2 15 cm2 30 cm2 30 cm2 18 cm2 Surface Area = 126 cm2

  23. Surface Area • Cylinder – (circular prism) a prism with two parallel, equal circles on opposite sides. To find the surface area of a cylinder we can add up the areas of the separate faces.

  24. Surface Area • In a cylinder there are a pair of opposite and equal circles. We can find the surface area of a cylinder by adding the areas of the two blue ends (A) and the yellow sides (B). A B

  25. Surface Area • We can find the area of the two ends (A) by using the formula for the area of a circle. • A = π r2 B =10 a 5

  26. Surface Area • Sketch cylinder and copy table. Work together to find the S.A.

  27. Surface Area • Sketch cylinder and copy table. Calculate S.A. • Assignment 4m 2m A A

  28. Volume Cylinder Area = π x r2 = π x 32 = π9cm2 3cm 5cm Volume = length x Area = 5 x π9cm2 = 5 x π x 9cm2 = 45 x π =45π

  29. Lets do these together. Find the volume. V = r2h 16 Volume of a Cylinder The volume, V, of a cylinder is V = Bh = r2h, where B is the area of the base, h is the height, and r is the radius of the base.

  30. 6cm 4cm 2cm 5cm Volume Trapezoid Prism trapezoid Area = ½ x(a + b) x h = ½ x (6 + 2)x 5 = ½ x 40cm2 = 20cm2 Volume = length x area = 20x 4 = 80cm3

  31. 8cm 4cm 2cm 4cm Volume Trapezoid Prism trapezoid Area = ½ x(a + b) x h = ½ x (8 + 3)x 4 = ½ x cm2 = 20cm2 Volume = length x area = 20x 4 = 80cm3

  32. Geometry Volume of Rectangular and Triangular Prisms

  33. Volume • The same principles apply to the triangular prism. To find the volume of the triangular prism, we must first find the area of the triangular base (shaded in yellow). h b

  34. Volume • To find the area of the Base… Area (triangle) = b x h 2 This gives us the Area of the Base (B). h b

  35. Volume • Now to find the volume… We must then multiply the area of the base (B) by the height (h) of the prism. This will give us the Volume of the Prism. B h

  36. Volume • Volume of a Triangular Prism Volume (triangular prism) V = B x h B h

  37. Volume Volume V = B x h • Together…

  38. Volume Volume V = B x h V = (8 x 4) x 12 2 • Together…

  39. Volume Volume V = B x h V = (8 x 4) x 12 2 V = 16 x 12 • Together…

  40. Volume Volume V = B x h V = (8 x 4) x 12 2 V = 16 x 12 V = 192 cm3 • Together…

  41. Volume Find the Volume • Your turn…

  42. Triangular Prism • To find the volumeof a triangular prism find the area of the triangular base and multiply times the height of the prism. The height will always be the distance between the two triangles.

  43. Volume Triangular Prism Cross-sectional Area = ½ x b x h = ½ x 8 x 4 = .5 x 32 = 16cm2 4cm 4.9cm 6cm 8cm Volume = length x CSA = 16 x 6 = 96cm3

  44. Find the Volume of the Triangular Prism. 4 4 10 10 ! 6 ! 8

  45. Volume Cuboid Cross-sectional Area = b x h = 7 x 5 = 35cm2 5cm 10cm 7cm Volume = length x CSA = 10 x 35 = 350cm3

  46. The box shown is 5 units long, 3 units wide, and 4 units high. How many unit cubes will fit in the box? What is the volume of the box? Ex. 1: Finding the Volume of a rectangular prism

  47. VOLUMES OF PRISMS AND CYLINDERS Volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure. 1cm How many 1cm3 cubes will fill the rectangular prism on the right

  48. 10 7 6 Find the volume. Volume of a Prism The volume, V, of a prism is V = Bh, where B is the area of the base and h is the height.

  49. Find the volume. V=s3 9 in. 9 in. 9 in. Volume of a Cube The volume of a cube is the length of its side cubed, or V=s3

  50. Volume of a cuboid Volume of a cuboid = length × width × height = lwh 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 length, l width, w

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