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Solid geometry ii slide

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Solid geometry ii slide

  1. 1. What shapecan you see?
  2. 2. SOLIDGEOMETRY II
  3. 3. LEARNING OUTCOMESState the geometric properties of prisms,pyramids, cylinders, cones and spheres.Draw nets for prisms, pyramids,cylinders and cones.State and find surface areas of prisms,pyramids, cylinders, cones and spheres.
  4. 4. DEFINITIONSolid geometry is concerned withthree-dimensional shapes.Some examples of three-dimensionalshapes are: • Prisms • Pyramids • Cylinders • Cones • Spheres
  5. 5. 12.1 PROPERTIES SOLIDS DESCRIPTION EXAMPLESPRISM A solid with two congruent, parallel bases which are polygons.PYRAMID A solid with a base which is a polygon and triangular sides that converge at a vertex.CYLINDER A solid with two parallel congruent circular faces and a curved surface.CONE A solid with a circular base and a vertex.SPHERE A solid having all of its points the same distance from its centre.
  6. 6. Rectangular PrismsTriangular PrismsHexagonal Prisms
  7. 7. Square Pyramids Rectangular PyramidTriangular Pyramid Hexagonal Pyramid
  8. 8. 5 faces8 edges5 vertices2 faces2 edges1 vertices 5 faces 9 edges 6 vertices
  9. 9. 12.2 NETS OF GEOMETRIC 12.2 NETS OF GEOMETRIC SOLIDS SOLIDSA net is a two-dimensionalfigure that can be foldedinto a three-dimensionalsolid.
  10. 10. EXAMPLE 11)2)
  11. 11. 3) 4)
  12. 12. WORKSHEET
  13. 13. 12.3 SURFACE AREAThe surface area of a solid is thetotal area of all the faces of thesolid.• It is measured using squares• Units include mm²,cm²,m²,km².
  14. 14. SOLIDS NETS SURFACE AREAPYRAMID Area of four triangular faces + Area of rectangular basePRISM Area of three rectangular faces + Area of two triangular faces
  15. 15. Example 1:Calculate the surface area of the pyramid shown.
  16. 16. SOLUTION Area of square base 13 cm = 10 × 10 = 100cm 2 10 cm Area of a triangular face 1 = ×10 ×12 = 60cm 2 2Surface area of the pyramid = 100 + (4 × 60) = 340cm 2
  17. 17. SURFACE AREA OF CYLINDER r r l hl = circumference of the base circle =2πrArea of curved surface (rectangular) + Area of two circular faces. = 2πrh + 2πr 2
  18. 18. ExampleFind the surface area of a cylinderwith a radius of 7 cm and a height of 2220 cm. (Take π= 7 )
  19. 19. SOLUTION r = 7cm h = 20cmSurface area of the cylinder = 2πr + 2πrh 2 22 2 22 = 2( )(7 ) + 2( )(7)(20) 7 7 = 308 + 880 = 1188cm 2
  20. 20. SURFACE AREA OF CONE l l r r Area of sector = π rl Area of circle = π 2 rArea of sector + Area of circle = πrl + πr 2
  21. 21. ExampleCalculate the surface area of a conewith a radius of 5 cm and a slantheight of 8 cm. (Take π = 3.142)
  22. 22. SOLUTION r = 5cm l = 8cmSurface area of the cone = πrl + πr 2 = (3.142)(5)(8) + (3.142)(52 ) = 204.23cm 2
  23. 23. SURFACE AREA OF SPHERESurface area of a sphere = 4πr 2Where r is the radius of the sphere
  24. 24. Example:Find the surface area of the sphere. 22(Take π = ) 7
  25. 25. SOLUTIONSurface area of the sphere: 22 = 4πr = 4 × × 3.52 = 154cm 2 2 7
  26. 26. POP QUIZ
  27. 27. 1) Find the surface area of the sphere that has 3 a) radius = 1 m 11 b) diameter = 2.8cm
  28. 28. SOLUTION 3a) r =1 11 2 22 14  4πr 2 = 4 × ×  7  11  = 20.3636b) Diameter = 2.82 22 2.8 2 4πr = 4 × 2 ×( ) = 24.64 7 2
  29. 29. 2) Find the value of h for the solid shown in the diagram if its surface area is 1551 cm 2 . 22 Take π= 7 21 cm h cm
  30. 30. SOLUTION 21The solid given is cylinder. r= h=? 2 2πr 2 + 2πrh = 1551  22  21  2   22 21   2 × ×    +  2 × × × h = 1551  7 2   7 2    693 + 66h = 1551 66h = 858 h = 13
  31. 31. 3) A cone has a base of diameter 14 cm. Find the slant height of the cone if its surface area 286 cm 2 . 22 Take π= 7
  32. 32. SOLUTIONDiameter =14 cm r=7 l =? πrl +πr 2 = 286  22   22  7 × 7 × s  +  × 7 2  = 286   7  22 s + 154 = 286 22l =132 l =6
  33. 33. 44) A sphere has a surface area of 804 mm 2. 7 What is its radius?
  34. 34. Let r be the radius of the sphere.Surface area of the sphere = 4πr 2 4 4π =804 mm 2 r 2 7 22 5632 4 × ×r = 2 7 7 88 2 5632 r = 7 7 r 2 = 64 r =8
  35. 35. 5) Calculate the value of x for the following solid. 10 cm x cm Surface area = 785 cm2
  36. 36. SOLUTIONr =10  22   22  πrl + πr 2 =  ×10 × l  +  ×10 2  = 785 7  7  220 2200 l+ = 785 7 7 220 3295 l= 7 7 l = 14.97
  37. 37. 6) 12 cm 5 cm Calculate the surface area of the cone
  38. 38. Solution 13 cm 12 cm 5 cmSurface area = 282.8571
  39. 39. 7) 2.8 mm If the diameter of the iron rod is 2.8 mm and the surface area of the rod is 2.8mm, find its length.
  40. 40. Solution r =1.4  22   22 22π rh + 2π r =  2 × × 1.4 × h +  2 × × (1.4)  = 892.32 2  7   7  8.8h +12.32 = 898.32 h = 100
  41. 41. Example 1Find the total surface area of thefollowing solid. Take π = 3.142 .
  42. 42. Example 2The solid shown below consists of acone and a hemisphere with a commonbase. What is the total surface area of =the solid? Take π3.142 . “Hemi” means half.
  43. 43. HOMEWORK• Ex12.3A, Ex12.3B, Ex12.3CNEXT LESSON Chapter 13 - Statisticshttp://www.harcourtschool.com/jingles/jingles_all/1what_am_i.html

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