surface area and volume

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surface area and volume

  1. 1. Slide show<br />On <br />Mathematics <br />Exercise 13<br />Topic on <br />Surface Area and Volume<br />
  2. 2. Surface Area and Volume<br />Vocabulary & Formulas<br />
  3. 3. Prism<br />Definition:<br />A three-dimensional solid that has two congruent and parallel faces that are polygons. The remaining faces are rectangles. Prisms are named by their faces.<br />
  4. 4. Rectangular Prism<br />Definition:<br />A three-dimensional solid that has two congruent and parallel faces that are rectangles. The remaining faces are rectangles.<br />
  5. 5. Cube<br />Definition:<br />A rectangular prism in which all faces are congruent squares.<br />
  6. 6. Surface Area<br />Definition:<br />The sum of the areas of all of the faces of a three-dimensional figure.<br />Ex. How much construction paper will I need to fit on the outside of the shape?<br />
  7. 7. Volume<br />Definition:<br />The measure in cubic units of the interior of a solid figure; or the space enclosed by a solid figure.<br />Ex. How much sand will it hold?<br />
  8. 8. Surface Area of a Rectangular Prism<br />Ex:<br />How much construction paper would I need to fit on the outside of a particular rectangular prism?<br />Formula:<br />S.A. = 2LW + 2Lh + 2Wh<br />
  9. 9. Surface Area of a Cube<br />Ex:<br />How much construction paper would I need to fit on the outside of a particular cube?<br />Formula:<br />S.A. = 6s2<br />
  10. 10. Volume of a Rectangular Prism<br />Ex:<br />How much sand would I need to fill the inside of a particular rectangular prism?<br />Formula:<br />V = L*W*h<br />
  11. 11. Volume of a Cube<br />Ex:<br />How much sand would I need to fill the inside of a particular cube?<br />Formula:<br />V = s3<br />
  12. 12. Surface area and volume of different Geometrical Figures<br />Cube<br />Cylinder<br />Parallelopiped<br />Cone<br />
  13. 13. face<br />face<br />face<br />1<br />Dice (Pasa)<br />3<br />2<br /> Faces of cube<br />Total faces = 6 ( Here three faces are visible)<br />
  14. 14. Face<br />Face<br />Face<br />Book<br />Brick<br />Faces of Parallelopiped<br />Total faces = 6 ( Here only three faces are visible.)<br />
  15. 15. Cores<br />Cores<br />Total cores = 12 ( Here only 9 cores are visible)<br />Note Same is in the case in parallelopiped.<br />
  16. 16. Surface area<br />Cube <br />Parallelopiped <br />c<br />a<br />b<br />a<br />a<br />Click to see the faces of parallelopiped.<br />a<br />(Here all the faces are rectangular)<br />(Here all the faces are square)<br />Surface area = Area of all six faces<br /> = 6a2<br />Surface area = Area of all six faces<br /> = 2(axb + bxc +cxa)<br />
  17. 17. Volume of Parallelopiped<br />Click to animate <br />c<br />b<br />b<br />a<br />Area of base (square) = a x b<br />Height of cube = c<br />Volume of cube = Area of base x height<br /> = (a x b) x c<br />
  18. 18. Volume of Cube<br />Click to see<br />a<br />a<br />a<br />Area of base (square) = a2<br />Height of cube = a<br />Volume of cube = Area of base x height<br /> = a2 x a = a3<br />(unit)3<br />
  19. 19. Outer Curved Surface area of cylinder<br />r<br />r<br />h<br />Click to animate <br />Activity -: Keep bangles of same radius one over another. It will form a cylinder.<br />Circumference of circle = 2 π r<br />Formation of Cylinder by bangles<br />It is the area covered by the outer surface of a cylinder.<br />Circumference of circle = 2 π r<br />Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)<br />
  20. 20. Total Surface area of a solid cylinder<br />Curved surface<br />circular surfaces<br />Area of curved surface +<br />area of two circular surfaces<br />=<br />=(2 π r) x( h) + 2 π r2<br />= 2 π r( h+ r)<br />
  21. 21. r<br /> Other method of Finding Surface area of cylinder with the help of paper<br />h<br />h<br />2πr<br />Surface area of cylinder = Area of rectangle= 2 πrh<br />
  22. 22. r<br />h<br />Volume of cylinder<br />Volume of cylinder = Area of base x vertical height<br />= π r2xh<br />
  23. 23. Cone<br />l = Slant height<br />h<br />Base<br />r<br />
  24. 24. Volume of a Cone<br />Click to See the experiment<br />h<br />h<br />Here the vertical height and radius of cylinder & cone are same.<br />r<br />r<br />3( volume of cone) = volume of cylinder<br />3( V) = π r2h<br />V = 1/3 π r2h<br />
  25. 25. if both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone ,<br />Volume = 3V<br /> Volume =V<br />
  26. 26. Mr. Mohan has only a little jar of juice he wants to distribute it to his three friends. This time he choose the cone shaped glass so that quantity of juice seem to appreciable. <br />
  27. 27. Surface area of cone<br />l<br />2πr<br />l<br />l<br />2πr<br />Area of a circle having sector (circumference) 2π l = π l 2<br />Area of circle having circumference 1 = π l 2/ 2 π l <br />So area of sector having sector 2 π r = (π l 2/ 2 π l )x 2 π r = π rl<br />
  28. 28. Comparison of Area and volume of different geometrical figures<br />
  29. 29. Area and volume of different geometrical figures<br />r<br />r<br />r<br />r/√2<br />l=2r<br />r<br />
  30. 30. Total surface Area and volume of different geometrical figures and nature<br />r<br />r<br />r<br />l=3r<br /> r<br />1.44r<br />22r<br />So for a given total surface area the volume of sphere is maximum. Generally most of the fruits in the nature are spherical in nature because it enables them to occupy less space but contains big amount of eating material.<br />
  31. 31. Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree<br />Click the next<br />
  32. 32. 3r<br />r<br />r<br />V= 1/3π r2(3r)<br />V= π r3<br />Long but Light in weight<br />Small niddle will require to stick it in the tree,so little harm in tree<br />V= π r2 (3r) <br />V= 3 π r3<br />Long but Heavy in weight<br />Long niddle will require to stick it in the tree,so much harm in tree<br />
  33. 33. Bottle<br />Cone shape<br />Cylindrical shape<br />
  34. 34. r<br /> V1<br />If we make a cone having radius and height equal to the radius of sphere. Then a water filled cone can fill the sphere in 4 times.<br />r<br />r<br />V=1/3 πr2h<br />If h = r then<br />V=1/3 πr3<br /> V1 = 4V = 4(1/3 πr3) <br />= 4/3 πr3<br />
  35. 35. Volume of a Sphere<br />Click to See the experiment<br />r<br />r<br />h=r<br />Here the vertical height and radius of cone are same as radius of sphere.<br />4( volume of cone) = volume of Sphere<br />4( 1/3πr2h) = 4( 1/3πr3 ) = V<br />V = 4/3 π r3<br />
  36. 36. Volume<br />is the amount of space occupied by any 3-dimensional object.<br />1cm<br />1cm<br />1cm<br />Volume = base area x height<br /> = 1cm2 x 1cm<br /> = 1cm2<br />
  37. 37. Back<br />Top<br />Side 2<br />Side 1<br />Front<br />Bottom<br />Cuboid<br />Back<br />Top<br />Side 2<br />Side 1<br />Front<br />Height (H)<br />Bottom<br />Breadth (B)<br />Length (L)<br />
  38. 38. The net<br />L<br />H<br />H<br />L<br />H<br />B<br />B<br />B<br />B<br />L<br />H<br />H<br />H<br />L<br />B<br />B<br />L<br />
  39. 39. Total surface Area<br />L<br />L<br />H<br />L<br />H<br />B<br />B<br />B<br />B<br />H<br />H<br />L<br />H<br />H<br />L<br />L<br />L<br />Total surface Area = L x H + B x H + L x H + B x H + L x B + L x B<br /> = 2 LxB + 2BxH + 2LxH<br /> = 2 ( LB + BH + LH )<br />
  40. 40.
  41. 41. Cube<br />L<br />L<br />L<br />Volume = Base area x height<br /> = L x L x L<br /> = L3<br /><ul><li>Total surface area = 2LxL + 2LxL + 2LxL</li></ul> = 6L2<br />
  42. 42. Sample net<br />Total surface area<br />Volume<br />Figure<br />Name<br />6L2<br />L3<br />Cube<br />2(LxB + BxH + LxH)<br />LxBxH<br />Cuboid<br />
  43. 43. Show ends<br />

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