Title: Surface area and volume of 3-dimensional Figures
1Surface area and volume of 3-dimensional Figures
2Cuboid A Cuboid has 6
faces..
Front
Top
Right Side
Front
Back
Each face is a rectangle.
Bottom
Right Side
Left Side
Front
Top
3 cube
Cube is also having 6 faces ( Here three faces
are visible)
4 Surface area
Cube
cuboid
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 Volume of cuboid
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 Volume of Cube
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
r
Curved Surface area of cylinder Area of
rectangle 2prh
8 Total Surface Area of a Cylinder
Area of curved surface
area of two circular surfaces
(2 p r) x( h) 2 p r2
2 p r( h r)
9 Volume of
cylinder
Volume of cylinder Area of base x vertical
height p r2 xh
10Curved Surface Area of Cone
Curved Surface Area of a Cone p r l
where l v ( r²h² )
11Volume 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 ) p r2h
V 1/3 p r2h
12If both cylinder and cone have same height and
radius then volume of a cylinder is three times
the volume of a cone ,
13Volume of a Sphere
Here the vertical height and radius of cone
are same as radius of sphere.
hr
4( volume of cone) volume of Sphere
4( 1/3pr2h ) 4( 1/3pr3 ) V
V 4/3 p r3
14 Comparison of Area and volume of
different geometrical figures
Surface area 6a2 2p rh p r l 4 p r2
Volume a3 p r2h 1/3p r2h 4/3 p r3
15 Method of finding Curved Surface area of
cylinder
Circumference of circle 2 p r
Formation of Cylinder by bangles
It is the area covered by the outer surface of a
cylinder.
Circumference of circle 2 p r Area covered by
cylinder curved Surface area of of cylinder
(2 p r)
x( h)