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- 1. What shapecan you see?
- 2. SOLIDGEOMETRY II
- 3. LEARNING OUTCOMESState 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. DEFINITIONSolid geometry is concerned withthree-dimensional shapes.Some examples of three-dimensionalshapes are: • Prisms • Pyramids • Cylinders • Cones • Spheres
- 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. Rectangular PrismsTriangular PrismsHexagonal Prisms
- 7. Square Pyramids Rectangular PyramidTriangular Pyramid Hexagonal Pyramid
- 8. 5 faces8 edges5 vertices2 faces2 edges1 vertices 5 faces 9 edges 6 vertices
- 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. EXAMPLE 11)2)
- 11. 3) 4)
- 12. WORKSHEET
- 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. SOLIDS NETS SURFACE AREAPYRAMID Area of four triangular faces + Area of rectangular basePRISM Area of three rectangular faces + Area of two triangular faces
- 15. Example 1:Calculate the surface area of the pyramid shown.
- 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. 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. ExampleFind the surface area of a cylinderwith a radius of 7 cm and a height of 2220 cm. (Take π= 7 )
- 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. 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. ExampleCalculate the surface area of a conewith a radius of 5 cm and a slantheight of 8 cm. (Take π = 3.142)
- 22. SOLUTION r = 5cm l = 8cmSurface area of the cone = πrl + πr 2 = (3.142)(5)(8) + (3.142)(52 ) = 204.23cm 2
- 23. SURFACE AREA OF SPHERESurface area of a sphere = 4πr 2Where r is the radius of the sphere
- 24. Example:Find the surface area of the sphere. 22(Take π = ) 7
- 25. SOLUTIONSurface area of the sphere: 22 = 4πr = 4 × × 3.52 = 154cm 2 2 7
- 26. POP QUIZ
- 27. 1) Find the surface area of the sphere that has 3 a) radius = 1 m 11 b) diameter = 2.8cm
- 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. 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. 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. 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. 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. 44) A sphere has a surface area of 804 mm 2. 7 What is its radius?
- 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. 5) Calculate the value of x for the following solid. 10 cm x cm Surface area = 785 cm2
- 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. 6) 12 cm 5 cm Calculate the surface area of the cone
- 38. Solution 13 cm 12 cm 5 cmSurface area = 282.8571
- 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. Solution r =1.4 22 22 22π rh + 2π r = 2 × × 1.4 × h + 2 × × (1.4) = 892.32 2 7 7 8.8h +12.32 = 898.32 h = 100
- 41. Example 1Find the total surface area of thefollowing solid. Take π = 3.142 .
- 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. 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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