Surface area and volume of 3-dimensional Figures

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Cuboid

A Cuboid has 6 faces..

Each face is a rectangle.

Front

faceface

face

Cube is also having 6 faces

( Here three faces are visible)

1

2 3

Dice (Pasa)

cube

Surface area = Area of all six faces

= 6a2

a

Surface area

Cube cuboid

Surface area = Area of all six faces

= 2(lxb + bxh +hxl)

a

a

a

(Here all the faces are square) (Here all the faces are rectangular)

h

lb

Area of base (Rectangle) = l x b

l

Height of cuboid = h

Volume of cuboid = Area of base x height = (l x b) x h

=lXbXh

h

Volume of cuboid

Front

b

Volume of Cube

a

a

Area of base (square) = a2

Height of cube = a

Volume of cube = Area of base x height

= a2 x a = a3

a

a

a

2πr

h

r

h

Curved Surface area of cylinder = Area of rectangle= 2πrh

Method of Finding Curved Surface area of Cylinder

r

Total Surface Area of a Cylinder

=(2 π r) x( h) + 2 π r2

Curved surface

Area of curved surface + area of two circular surfaces

circular surfaces

= 2 π r( h+ r)

Volume of cylinder

Volume of cylinder = Area of base x vertical height

= π r2 xh

r

h

Curved Surface Area of Cone

Baser

h

l = Slant height

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

3( V ) = π r2h

r

h h

r

Volume of a Cone

Here the vertical height and radius of cylinder & cone are same.

3( volume of cone) = volume of cylinder

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

4( 1/3πr2h ) = 4( 1/3πr3 ) = V

h=rr

Volume of a Sphere

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 r3

r

Surface area

6a2 2π rh π r l 4 π r2

Volume a3 π r2h 1/3π r2h 4/3 π r3

Comparison of Area and volume of different geometrical figures

Circumference of circle = 2 π r

Area covered by cylinder = curved Surface area of of cylinder

= (2 π r) x( h)

r h

Method of finding Curved Surface area of 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