Transcript Document

Surface area and volume of different Geometrical Figures
Cube
Parallelopiped
Cylinder
Cone
Faces of cube
face
face
face
1
2
3
Dice (Pasa)
Total faces = 6 ( Here three faces are visible)
Faces of Parallelopiped
Face
Face
Face
Total faces = 6 ( Here only three faces are visible.)
Book
Brick
Cores
Cores
Total cores = 12 ( Here only 9 cores are visible)
Note Same is in the case in parallelopiped.
Surface area
Cube
Parallelopiped
c
a
b
a
a
Click to see the faces of
parallelopiped.
a
(Here all the faces are square)
Surface area = Area of all six faces
= 6a2
(Here all the faces are rectangular)
Surface area = Area of all six faces
=
2(axb + bxc +cxa)
Volume of Parallelopiped
Click to animate
c
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
Volume of Cube
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
Click to see
Outer Curved Surface area of cylinder
r
r
Circumference of
circle = 2 π r
h
Click to animate
Activity -: Keep
bangles of same
radius one over
another. It
will
form a cylinder.
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
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)
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
Volume of cylinder
r
h
Volume of cylinder = Area of base x vertical height
= π r2 xh
Cone
h
Base
r
Click to See
the experiment
Volume of a Cone
h
Here the vertical height and
radius of cylinder & cone are
same.
h
r
r
3( volume of cone) = volume of cylinder
3( V )
= π r2h
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.
Surface area of cone
l
2πr
l
l
Area of a circle having sector (circumference) 2π l = π l 2
2πr
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
Comparison of Area and volume of different geometrical figures
Surface
area
6a2
2π rh
πrl
4 π r2
Volume
a3
π r 2h
1/3π r2h
4/3 π r3
Area and volume of different geometrical figures
r
r
r
r
Surface
area
r/√2
6r2
=2 π r2
l=2r
2π r2
2π r2
2 π r2
3.14 r3
0.57π r3
0.47π r3
(about)
Volume
r3
Total surface Area and volume of different geometrical figures and nature
r
r
r
1.44r
r
22r
l=3r
Total
Surface
area
4π r2
4π r2
4π r2
4 π r2
Volume
2.99r3
3.14 r3
2.95 r3
4.18 r3
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.
Think :- Which shape (cone or cylindrical) is better for collecting
resin from the tree
Click the next
r
r
3r
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
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
r
V=1/3 πr2h
V1
If h = r then
V=1/3 πr3
V1 = 4V = 4(1/3 πr3)
= 4/3 πr3
Click to See
the experiment
Volume of a Sphere
h=r
r
Here the vertical height and
radius of cone are same as
radius of sphere.
r
4( volume of cone) = volume of Sphere
4( 1/3πr2h ) = 4( 1/3πr3 ) = V
V = 4/3 π r3
Thanks