Presentation on theme: "Surface area and volume of different Geometrical Figures"— Presentation transcript:
1 Surface area and volume of different Geometrical Figures CubeParallelopipedCylinderCone
2 Faces of cube face 1 3 2 Dice (Pasa) Total faces = 6 ( Here three faces are visible)
3 Faces of Parallelopiped Total faces = 6 ( Here only three faces are visible.)BookBrick
4 Cores Cores Total cores = 12 ( Here only 9 cores are visible) Note Same is in the case in parallelopiped.
5 (Here all the faces are rectangular) (Here all the faces are square) Surface areaCubeParallelopipedcabaaClick to see the faces of parallelopiped.a(Here all the faces are rectangular)(Here all the faces are square)Surface area = Area of all six faces= 6a2Surface area = Area of all six faces= 2(axb + bxc +cxa)
6 Volume of Parallelopiped Click to animatebcbaArea of base (square) = a x bHeight of cube = cVolume of cube = Area of base x height= (a x b) x c
7 Area of base (square) = a2 Volume of CubeClick to seeaaArea of base (square) = a2Height of cube = aVolume of cube = Area of base x height= a2 x a = a3(unit)3
8 Outer Curved Surface area of cylinder Click to animateActivity -: Keep bangles of same radius one over another. It will form a cylinder.hrrCircumference of circle = 2 π rFormation of Cylinder by banglesIt is the area covered by the outer surface of a cylinder.Circumference of circle = 2 π rArea covered by cylinder = Surface area of of cylinder = (2 π r) x( h)
9 Total Surface area of a solid cylinder circular surfacesCurved surface=Area of curved surface +area of two circular surfaces=(2 π r) x( h) + 2 π r2= 2 π r( h+ r)
10 Other method of Finding Surface area of cylinder with the help of paper Surface area of cylinder = Area of rectangle= 2 πrh
11 Volume of cylinder = Area of base x vertical height = π r2 xh
13 Volume of a Cone Click to See the experiment h h Here the vertical height and radius of cylinder & cone are same.rr3( volume of cone) = volume of cylinder3( V ) = π r2hV = 1/3 π r2h
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 = 3VVolume =V
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 Surface area of cone l 2πr l l Area of a circle having sector (circumference) 2π l = π l 2Area of circle having circumference 1 = π l 2/ 2 π lSo area of sector having sector 2 π r = (π l 2/ 2 π l )x 2 π r = π rl
17 6a2 2π rh π r l 4 π r2 a3 π r2h 1/3π r2h 4/3 π r3 Surface area Volume Comparison of Area and volume of different geometrical figuresSurface area6a22π rhπ r l4 π r2Volumea3π r2h1/3π r2h4/3 π r3
18 6r2 =2 π r2 (about) 2π r2 2 π r2 r3 3.14 r3 0.57π r3 0.47π r3 r r/√2 r Area and volume of different geometrical figuresrl=2rrr/√2rSurface area6r2=2 π r2(about)2π r22 π r2Volumer33.14 r30.57π r30.47π r3
19 4π r2 4 π r2 2.99r3 3.14 r3 2.95 r3 4.18 r3 r r Total Surface area r Total surface Area and volume of different geometrical figures and naturerl=3rrr1.44r22rTotal Surface area4π r24 π r2Volume2.99r33.14 r32.95 r34.18 r3So 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.
20 Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree Click the next
21 Long but Light in weight rr3rV= 1/3π r2(3r)V= π r3Long but Light in weightSmall niddle will require to stick it in the tree,so little harm in treeV= π r2 (3r)V= 3 π r3Long but Heavy in weightLong niddle will require to stick it in the tree,so much harm in tree
23 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.V1rrrV=1/3 πr2hIf h = r thenV=1/3 πr3V1 = 4V = 4(1/3 πr3)= 4/3 πr3
24 Volume of a Sphere Click to See the experiment h=r r Here the vertical height and radius of cone are same as radius of sphere.4( volume of cone) = volume of Sphere4( 1/3πr2h ) = 4( 1/3πr3 ) = VV = 4/3 π r3