Surface area and volume of different Geometrical Figures

Surface area and volume of different Geometrical Figures Cube Cuboid Cylinder Cone

Faces of cube face 1 2 3 Dice Total faces = 6 ( Here three faces are visible)

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

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

Surface area Cube Cuboid c a b a a Click to see the faces of parallelopiped. a (Here all the faces are square) Surface area = Area of all six faces = 6 a 2 (Here all the faces are rectangular) Surface area = Area of all six faces = 2(axb + bxc +cxa)

Volume of Cuboid Click to animate c b a Area of base (square) = a x b Height of cube = c Volume of cube = Area of base x height = (a x b) x c b

Volume of Cube a 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 (unit)3 Click to see

Outer Curved Surface area of cylinder r Circumference of circle = 2 π r r h Click to animate Activity -: Keep bangles of same radius one over another. It will form a cylinder. Formation of Cylinder by bangles It is the area covered by the outer surface of a cylinder. Circumference of circle = 2 π r Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)

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

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

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

Cone l= Sla eig nt h ht h Base r

Click to See the experiment Volume of a Cone h Here the vertical height and radius of cylinder & cone are same. r 3( volume of cone) = volume of cylinder 3( V ) V = 1/3 π r 2 h = π r 2 h h r

if both cylinder and cone have same height and radius then volume of a cylinder is three times the volume of a cone , Volume = 3 V 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.

Surface area of cone l 2πr l l Area of a circle having sector (circumference) 2π l = π l 2 2πr 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

Comparison of Area and volume of different geometrical figures Surface area 6 a 2 2π rh πrl 4 π r 2 Volume a 3 π r 2 h 1/3π r 2 h 4/3 π r 3

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

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

r r 3 r V= 1/3π r 2(3 r) 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 (3 r) 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

Bottle Cone shape Cylindrical shape

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. r r r V=1/3 πr 2 h V 1 If h = r then V=1/3 πr 3 V 1 = 4 V = 4(1/3 πr 3) = 4/3 πr 3

Click to See the experiment Volume of a Sphere h=r r Here the vertical height and radius of cone are same as radius of sphere. r 4( volume of cone) = volume of Sphere 4( 1/3πr 2 h ) = 4( 1/3πr 3 ) = V V = 4/3 π r 3

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