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1. Assignment (FA-3)
Submitted to :- Sh. BharatBhushan Sir
Submitted by :- Nitin Chhaperwal
Class IX
Roll No. 915
Kendriya Vidyalaya SSTPS
Topic – Surface
Areas and Volumes

2. Contents :-

3. CUBE AND CUBOID

4. face
face
face
Total faces = 6 ( Here three faces are visible)
1
2 3
Dice (Pasa)
Faces of cube

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

6. Cores
Total cores = 12 ( Here only 9 cores are visible)
Cores
Note Same is in the case in parallelopiped.

7. Surface area = Area of all six faces
= 6a2
a
b
Surface area
Cube Parallelopiped (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)

8. Area of base (rectangle) = a x b
a
Height of cuboid = c
Volume of cube = Area of base x height
= (a x b) x c
b
c
b
Volume of Parallelopiped Click to animate

9. 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

10. CYLINDER

11. Circumference of circle = 2 π r
Area covered by cylinder = Surface area 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

12. 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)

13. 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

14. Volume of cylinder
Volume of cylinder = Area of base x vertical height
= π r2
x h
r
h

15. Base
r
h
l=Slantheight
CONE

16. 3( V ) = π r2
h
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 r2
h

17. 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

18. 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.

19. 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

20. Think :- Which shape (cone or cylindrical) is better for
collecting resin from the tree?
Click the next

21. 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
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
r

22. SPHERE

23. A sphere is the set of points in three
dimensions that are a fixed distance from
a given point, the center. A plane that
intersects a sphere through its center
divides the two halves or hemispheres.
The edge of a hemisphere is a great
circle.
Sphere

24. The volume of a hemisphere is
exactly halfway between the
volume of a cone and a cylinder
with the same radius r and
height equal to r.

26. V1
r
V=1/3 πr2
h
If h = r then
V=1/3 πr3
r
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

27. 4( 1/3πr2
h ) = 4( 1/3πr3
) = V
h=r
r
Volume of a Sphere
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
Click to See
the experiment

28. The surface area of a sphere is four
times the area of a great circle.
≈ 50.3 units2

29. THANK YOU