Surface area and volume of different Geometrical Figures SphereCylinderCone

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 r3r r π r π r 3 Area and volume of different geometrical figures r/√ 2 r l=2r r r r

Total Surface area 4π r24π r2 4π r 2 Volume 2.99r r r r 3 Total surface Area and volume of different geometrical figures and nature r r l=3r r r 1.44r 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

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 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

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