Surface area and volume of different Geometrical Figures CubeCuboid CylinderCone

face Total faces = 6 ( Here three faces are visible) Dice Faces of cube

Faces of a Cuboid Brick Book Face Total faces = 6 ( Here only three faces are visible.)

Cores Total edges = 12 ( Here only 9 edges are visible) Edges Note  Same is in the case in Cuboid

Surface area = Area of all six faces = 6a 2 a b Surface area Cube Cuboid 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)

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 b c b Volume of CuboidClick to animate

Volume of Cube a a 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 a (unit) 3

Circumference of circle = 2 π r Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h) r 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 r Click to animate

Total Surface area of a solid cylinder =(2 π r) x( h) + 2 π r 2 Curved surface Area of curved surface +area of two circular surfaces= circular surfaces = 2 π r( h+ r)

2πr2πr h r h Surface area of cylinder = Area of rectangle= 2 πrh Other method of Finding Surface area of cylinder with the help of paper

Volume of cylinder Volume of cylinder = Area of base x vertical height = π r 2 xh r h

Cone Base r h l = Slant height

3( V ) = π r 2 h r hh 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

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

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.

l 2πr2πr l 2πr2πr l 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

Surface area 6a 2 2π rhπ r l4 π r 2 Volume a3a3 π r 2 h1/3π r 2 h4/3 π r 3 Comparison of Area and volume of different geometrical figures

Surface area 6r 2 = 2 π r 2 (about) 2π r 2 Volume r3r3 π r 3 π /3 π r 3 2/3 π r 3 Area and volume of different geometrical figures r/√ 2 r l=2r r r r

Think :- Which shape (cone or cylindrical) is better for collecting resin from the tree Click the next

r 3r V= 1/3π r 2 (3r) V= π r 3 Long but Light in weight Small needle 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 needle will require to stick it in the tree,so much harm in tree r

Cone shape Cylindrical shape Bottle

V1 r V=1/3 πr 2 h If h = r then V=1/3 πr 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 πr 3

4( 1/3 π r 2 h ) = 4( 1/3πr 3 ) = V h=r 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

Thanks U.C. Pandey R.C.Rauthan, G.C.Kandpal