PRESENTED BY-

Puneet kakkar

Faraz ali khan

Mayank gangwar

Hazi rizwan

Faiz ali

Amit bhatt

Harvinder singh

Contents-Contents- CUBECUBE CUBOIDCUBOID

CYLINDER CYLINDER CONECONE

SPHERE HEMISPHERESPHERE HEMISPHERE

FRUSTUM OF CONEFRUSTUM OF CONE

See and appreciate first the following pictures. Be

amazed and have fun!

See how strange are

they? That is how geometry

is applied.

Geometric Solids in Three DimensionsGeometric Solids in Three Dimensions

Height

Length Width

SURFACES OF A CUBE

CubeCube

• Volume = Base area x height= L x L x L= L3

L

L

L

• Total surface area = 2LxL + 2LxL + 2LxL

= 6L2

Curved surface Area=2LXL + 2LXL

=4L2

Why the farmers in Japan growwatermelons in the shape of cube?

WEIRD OR WHAT??????

Why the farmers of Japan grew watermelons in the shape of cube?

Huge Watermelons in cube shape facilitates efficient storage and refrigeration!!

Good enough! For the same reason our “tea pack” and “match box” come in this shape.

“Storage

Friendly

shapes !!”

“godly shapes !!”

Side 2

Bottom

Back

Top

Side 1Front

Side 2

Bottom

Back

Top

Side 1Front

Length (L)Breadth (B)

Height (H)

Cuboid

CUBOIDCUBOID FRONT

BACK

BASE

LEFT RIGHT

TOP

LB

H

VOLUME OF CUBOID = Length x Breadth x Height = LBH

CSA OF CUBOID = 2 Height [Length + breadth] = 2h[l+b]

TSA OF CUBOID= 2[ LB + BH + HL]

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

1 cm

B=2cm L= 3cm

H=

3cm

LET DIMENSIONS OF CUBOID BE-

Length= 3cm

Breadth= 2cm

Height= 3cm

Therefore volume of this cuboid-

= L X B X H

=3cm X 2cm X 3cm

= 18 cubic cm.

this volume is also equals to-

= 18 x volume of cube of side 1cm………

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)

Volume of cylinder

Volume of cylinder = Area of base x vertical height

= π r2 X h

r

hr

Area= π r2

Surface area of cone

Baser

h

L = S

lant h

eigh

t

2πr

l

2πr

l

l

2πr

l

2πr

l

Surface area of cone

CSA OF CONE = π r l

TSA OF CONE= π r l + π r2

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

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.

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

BUCKETS are frustum of cone

Combination of some 3d figures

A funnel is combination of two Frustums Or a frustum and a cylinder…..

A shuttle cock is combinationOf a frustum and a hemishere

Rocket is a combination of cone and cylinder

Football is in the form of sphere

Bowls are in the formOf hemisphere…..