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Surface area and volume of different Geometrical Figures - PowerPoint PPT Presentation


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Cube. Parallelopiped. Cylinder. Cone. Surface area and volume of different Geometrical Figures. Faces of cube. face. face. face. 1. Dice (Pasa). 3. 2. Total faces = 6 ( Here three faces are visible). Faces of Parallelopiped. Face.

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Presentation Transcript
slide2

Faces of cube

face

face

face

1

Dice (Pasa)

3

2

Total faces = 6 ( Here three faces are visible)

slide3

Faces of Parallelopiped

Face

Face

Face

Book

Brick

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

slide4

Cores

Cores

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

Note Same is in the case in parallelopiped.

slide5

Surface area

Cube

Parallelopiped

c

a

b

a

a

Click to see the faces of parallelopiped.

a

(Here all the faces are rectangular)

(Here all the faces are square)

Surface area = Area of all six faces

= 6a2

Surface area = Area of all six faces

= 2(axb + bxc +cxa)

slide6

Volume of Parallelopiped

Click to animate

c

b

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

slide7

Volume of Cube

Click to see

a

a

a

Area of base (square) = a2

Height of cube = a

Volume of cube = Area of base x height

= a2 x a = a3

(unit)3

slide8

Outer Curved Surface area of cylinder

r

r

h

Click to animate

Activity -: Keep bangles of same radius one over another. It will form a 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 = Surface area of of cylinder = (2 π r) x( h)

slide9

Total Surface area of a solid cylinder

Curved surface

circular surfaces

=

Area of curved surface +

area of two circular surfaces

=(2 π r) x( h) + 2 π r2

= 2 π r( h+ r)

slide10

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

r

h

h

2πr

Surface area of cylinder = Area of rectangle= 2 πrh

slide11

Volume of cylinder

r

h

Volume of cylinder = Area of base x vertical height

= π r2 xh

slide12

Cone

l = Slant height

h

Base

r

slide13

Volume of a Cone

Click to See the experiment

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

slide14

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

slide15

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.

slide16

Surface area of cone

l

2πr

l

l

2πr

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

slide18

Area and volume of different geometrical figures

r

r

r

r/√2

l=2r

r

slide19

Total surface Area and volume of different geometrical figures and nature

r

r

r

r

l=3r

1.44r

22r

So for a given total surface area the volume of sphere is maximum. Generally most of the fruits in the nature are spherical in nature because it enables them to occupy less space but contains big amount of eating material.

slide20

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

Click the next

slide21

3r

r

r

V= 1/3π r2(3r)

V= π r3

Long but Light in weight

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

slide22

Bottle

Cone shape

Cylindrical shape

slide23

r

V1

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 πr2h

If h = r then

V=1/3 πr3

V1 = 4V = 4(1/3 πr3)

= 4/3 πr3

slide24

Volume of a Sphere

Click to See the experiment

r

r

h=r

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

4( volume of cone) = volume of Sphere

4( 1/3πr2h) = 4( 1/3πr3 ) = V

V = 4/3 π r3

slide25

Thanks

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