Surface area and volume of different Geometrical Figures

Cube Cuboid Cylinder Cone

Faces of cube

face face 2 1 3 Dice

Total faces = 6 ( Here three faces are visible)

Faces of a Cuboid Face Face Total faces = 6 ( Here only three faces are visible.) Book Brick

Cores

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



Same is in the case in Cuboid

Cube Surface area Cuboid

a a a

(Here all the faces are square)

c b a Click to see the faces of parallelopiped.

(Here all the faces are rectangular) Surface area = Area of all six faces = 6a 2 Surface area = Area of all six faces = 2(axb + bxc +cxa)

Volume of Cuboid

b

a Area of base (square) = a x b Height of cube = c Volume of cube = Area of base x height = (a x b) x c b c

Click to animate

Volume of Cube

a a a

Area of base (square) = a 2 Height of cube = a Volume of cube = Area of base x height = a 2 x a = a 3

(unit) 3 Click to see

Outer Curved Surface area of cylinder

Click to animate r r h

Activity

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

will 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 = Surface area of of cylinder = (2 π r) x( h)

Total Surface area of a solid cylinder circular surfaces Curved surface

= Area of curved surface + area of two circular surfaces

=

(2 π r) x( h) + 2 π r 2 = 2 π r( h+ r)

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

h 2

π r

Surface area of cylinder = Area of rectangle= 2 πrh

Volume of cylinder

r h

Volume of cylinder = Area of base x vertical height = π r 2 xh

Base

Cone

h r

Volume of a Cone

Click to See the experiment r h

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

3( volume of cone) = volume of cylinder 3( V ) = π r 2 h V = 1/3 π r 2 h

h r

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.

Surface area of cone l Area of a circle having sector (circumference) 2 π l = π l 2 Area of circle having circumference 1 = π l 2 / 2 π l

2 π

So area of sector having sector 2 π r = (π l 2 / 2 π l )x 2 π r = π rl

r 2 π r l l

Comparison of Area and volume of different geometrical figures Surface area

6a 2

2 π rh π r l

4

π r

2 Volume

a 3

π r

2

h 1/3 π r

2

h

4/3

π r

3

Area and volume of different geometrical figures r Surface area

6r 2 = 2

π

r 2 (about)

2 π r

2 Volume

r 3

π r

3 r r

2 π r

2 r l=2r

2

π r

2 r/√ 2

π

/3

π r

3

2/3 π r

3

Think :-

Which shape (cone or cylindrical) is better for collecting resin from the tree Click the next

r r 3r V= 1/3 π r 2 (3r) V= π r 3 Long but Light in weight Small needle will require to stick it in the tree,so little harm in tree V= π r 2 (3r) V= 3 π r 3 Long but Heavy in weight

Long

needle

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

Bottle

Cone shape Cylindrical shape

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.

r r

V=1/3

πr 2 h If h = r then

V=1/3 πr 3

V1 = 4V = 4(1/3 π r 3 ) = 4/3 πr 3 V1 r

Volume of a Sphere

Click to See the experiment r

Here the vertical height and radius of cone are same as radius of sphere.

4( volume of cone) = volume of Sphere 4( 1/3 π r 2 h ) = 4( 1/3 πr 3 ) = V V = 4/3 π r 3

h=r r

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