Surface area and volume of 3-dimensional Figures

Each face is a rectangle. Cuboid A Cuboid has 6 faces.. Front Top Right Side Front Back Each face is a rectangle. Left Side Bottom Right Side Front Top

Cube is also having 6 faces ( Here three faces are visible) 1 2 3 Dice (Pasa) Cube is also having 6 faces ( Here three faces are visible)

Cube cuboid Surface area a a a h a b l (Here all the faces are square) (Here all the faces are rectangular) Surface area = Area of all six faces = 6a2 Surface area = Area of all six faces = 2(lxb + bxh +hxl)

=lXbXh Volume of cuboid Area of base (Rectangle) = l x b Front b l Area of base (Rectangle) = l x b Height of cuboid = h Volume of cuboid = Area of base x height = (l x b) x h =lXbXh

Area of base (square) = a2 Volume of Cube a a a a Area of base (square) = a2 Height of cube = a Volume of cube = Area of base x height = a2 x a = a3

Method of Finding Curved Surface area of Cylinder Curved Surface area of cylinder = Area of rectangle= 2πrh

Total Surface Area of a Cylinder circular surfaces Curved surface Area of curved surface + area of two circular surfaces =(2 π r) x( h) + 2 π r2 = 2 π r( h+ r)

Volume of cylinder = Area of base x vertical height = π r2 xh

Curved Surface Area of Cone Base r h l = Slant height Curved Surface Area of a Cone = π r l where l = √ ( r²+h² )

Volume of a Cone h h Here the vertical height and radius of cylinder & cone are same. r r 3( volume of cone) = volume of cylinder 3( V ) = π r2h V = 1/3 π r2h

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

Volume of a Sphere Here the vertical height and radius of cone are same as radius of sphere. r h=r r 4( volume of cone) = volume of Sphere 4( 1/3πr2h ) = 4( 1/3πr3 ) = V V = 4/3 π r3

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 figures Surface area 6a2 2π rh π r l 4 π r2 Volume a3 π r2h 1/3π r2h 4/3 π r3

Method of finding Curved Surface area of cylinder Circumference of circle = 2 π r 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 = curved Surface area of of cylinder = (2 π r) x( h)