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### maths presentation

1. 1. Surface area and volume of different Geometrical Figures Cube Parallelopiped Cylinder Cone
2. 2. Total faces = 6 ( Here three faces are visible) Faces of cube face face face 1 2 3 Dice (Pasa)
3. 3. Faces of Parallelopiped Total faces = 6 ( Here only three faces are visible.) Brick Book Face Face Face
4. 4. Total cores = 12 ( Here only 9 cores are visible) Cores Note  Same is in the case in parallelopiped. Cores
5. 5. Surface area = Area of all six faces = 6a 2 a b Surface area Cube Parallelopiped Surface area = Area of all six faces = 2(axb + bxc +cxa) c a a a Click to see the faces of parallelopiped. (Here all the faces are square) (Here all the faces are rectangular)
6. 6. Area of base (square) = a x b a Height of cube = c Volume of cube = Area of base x height = (a x b) x c Volume of Parallelopiped Click to animate b c b
7. 7. Volume of Cube Area of base (square) = a 2 Height of cube = a Volume of cube = Area of base x height = a 2 x a = a 3 Click to see (unit) 3 a a a
8. 8. Circumference of circle = 2 π r Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h) Outer Curved Surface area of cylinder Activity -: Keep bangles of same radius one over another. It will form a cylinder. It is the area covered by the outer surface of a cylinder. Formation of Cylinder by bangles Circumference of circle = 2 π r Click to animate r h r
9. 9. Total Surface area of a solid cylinder = (2 π r) x( h) + 2 π r 2 Area of curved surface + area of two circular surfaces = = 2 π r( h+ r) Curved surface circular surfaces
10. 10. Surface area of cylinder = Area of rectangle= 2 π rh Other method of Finding Surface area of cylinder with the help of paper 2 π r h r h
11. 11. Volume of cylinder Volume of cylinder = Area of base x vertical height = π r 2 xh r h
12. 12. Cone Base r h l = Slant height
13. 13. 3( V ) = π r 2 h r h h r Volume of a Cone Click to See the experiment Here the vertical height and radius of cylinder & cone are same. 3( volume of cone) = volume of cylinder V = 1/3 π r 2 h
14. 14. if both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone , Volume = 3V Volume =V
15. 15. 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.
16. 16. Area of a circle having sector (circumference) 2 π l = π l 2 Area of circle having circumference 1 = π l 2 / 2 π l So area of sector having sector 2 π r = ( π l 2 / 2 π l )x 2 π r = π rl Surface area of cone l 2 π r l 2 π r l
17. 17. Comparison of Area and volume of different geometrical figures Surface area 6a 2 2 π rh π r l 4 π r 2 Volume a 3 π r 2 h 1/3 π r 2 h 4/3 π r 3
18. 18. Area and volume of different geometrical figures Surface area 6r 2 = 2 π r 2 (about) 2 π r 2 2 π r 2 2 π r 2 Volume r 3 3.14 r 3 0.57 π r 3 0.47 π r 3 r/√ 2 r l=2r r r r
19. 19. Total surface Area and volume of different geometrical figures and nature 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. 2  2r Total Surface area 4 π r 2 4 π r 2 4 π r 2 4 π r 2 Volume 2.99r 3 3.14 r 3 2.95 r 3 4.18 r 3 r r l=3r r r 1.44r
20. 20. Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree Click the next
21. 21. r V= 1/3 π r 2 (3r) V= π r 3 Long but Light in weight Small niddle will require to stick it in the tree,so little harm in tree V= π r 2 (3r) V= 3 π r 3 Long but Heavy in weight Long niddle will require to stick it in the tree,so much harm in tree r 3r
22. 22. Cone shape Cylindrical shape Bottle
23. 23. V=1/3 π r 2 h If h = r then V=1/3 π r 3 r r 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. V1 = 4V = 4(1/3 π r 3 ) = 4/3 π r 3 V1 r
24. 24. 4( 1/3 π r 2 h ) = 4( 1/3 π r 3 ) = V h=r Volume of a Sphere Click to See the experiment Here the vertical height and radius of cone are same as radius of sphere. 4( volume of cone) = volume of Sphere V = 4/3 π r 3 r r
25. 25. Thanks U.C. Pandey R.C.Rauthan, G.C.Kandpal