1. Surface area and volume of 3-dimensional Figures

2. 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

3. 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)

4. 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)

5. =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

6. 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

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

8. 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)

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

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

11. 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

12. 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

13. 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

14. 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

15. 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)