Surface area and volume of different Geometrical Figures

Cube CuboidCylinder Cone

faceface

face

Total faces = 6 ( Here three faces are visible)

1

2 3

Dice

Faces of cube

Faces of a Cuboid

Brick

Book

Fac

e

Face

Face

Total faces = 6 ( Here only three faces are visible.)

Cores

Total edges = 12 ( Here only 9 edges are visible)

Edges

Note Same is in the case in Cuboid

Surface area = Area of all six faces

= 6a2

ab

Surface areaCube Cuboid

Surface area = Area of all six faces

= 2(axb + bxc +cxa)

c

a

a

a

Click to see the faces of parallelopiped.

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

Area of base (square) = a x b

a

Height of cube = c

Volume of cube = Area of base x height

= (a x b) x c

b

c

b

Volume of Cuboid Click to animate

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

Click to see

a

(unit)3

Circumference of circle = 2 π r

Area covered by cylinder = Surface area of of cylinder = (2 π r) x( h)

r h

Outer Curved Surface area of cylinder

Activity -: Keep bangles of same radius one over another. It will form a 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

Click to animate

Total Surface area of a solid 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)

2πr

h

r

h

Surface area of cylinder = Area of rectangle= 2 πrh

Other method of Finding Surface area of cylinder with the help of paper

Volume of cylinder

Volume of cylinder = Area of base x vertical height

= π r2 xh

r

h

Cone

Baser

h

l = Slant height

3( V ) = π r2h

r

h h

r

Volume of a Cone Click to See the experiment

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

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.

l

2πr

l

2πr

l

Area of a circle having sector (circumference) 2π l = π l 2

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

Surface area of cone

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

Surface area

6r2

=2 π r2

(about)

2π r2 2π r2 2 π r2

Volume r3 π r3 π /3 π r3 2/3 π r3

Area and volume of different geometrical figures

r/√2

r

l=2rr

r

r

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

Click the next

r

3r

V= 1/3π r2(3r)

V= π r3

Long but Light in weight

Small needle will require to stick it in the tree,so little harm in tree

V= π r2 (3r)

V= 3 π r3

Long but Heavy in

weight

Long needle will require to stick it in the tree,so much harm in tree

r

Cone shape

Cylindrical shape

Bottle

V1

r

V=1/3 πr2h

If h = r thenV=1/3 πr3

rr

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.

V1 = 4V = 4(1/3 πr3)

= 4/3 πr3

4( 1/3πr2h ) = 4( 1/3πr3 ) = V

h=rr

Volume of a Sphere Click to See the experiment

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

Thanks

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