The document presents an introduction to different geometric shapes including cubes, cuboids, cylinders, cones, spheres, and hemispheres, focusing on their surface areas and volumes. It explains the calculations for total surface area and volume for each shape with relevant formulas. Real-life applications of these geometric concepts, such as gift wrapping and filling containers, are also highlighted.

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THE
PRESENTATION
BEGINS

11. UMESH SIR

13.  INTRODUCTION
 CUBE
 CUBOID
 RIGHT CIRCULAR CYLINDER
 RIGHT CIRCULAR CONE
 SPHERE
 HEMISPHERE

14.  Have you ever wrapped a birthday gift?
If so, then you've covered the surface
area of a polyhedron with wrapping
paper.
 Have you ever poured a glass of milk?
If so, then you've filled the volume of a
glass with milk.
Not only this, but in day-to-day life, we
come across many activities which
involve the concept of surface areas and
volume.

15.  Surface Area of an object refers to the
total area of all its surfaces.
 For example : The amount of paper
required to wrap a gift gives us an idea
of surface area of gift.

16.  Volume of a solid
object refers to the
amount of space it
occupies or
contains.
 For example : The
amount of water a
swimming pool can
hold gives us an
idea of the volume
of the swimming
pool.

18. SURFACE
AREAIf each edge of cube is a units, its
Total surface area = 6a2 sq. units
Area of the faces leaving the top
And the bottom ones is known as
Its L.S.A. (Lateral Surface Area).
L.S.A. of cube = 4a2 sq. units

19. VOLUME
Volume of a
cube of
edge a
units is a3
cubic units.

21. TOTAL SURFACE
AREA Surface area of a
cuboid =
2 × lb Top and bottom
+ 2 × bh Front and back
+ 2 × lh Left and right side
= 2(lb + bh + lh)
h
l
b

22. LATERAL SURFACE
AREA
L.S.A. of cuboid =
T.S.A. – Area of
top and base
= 2(lb + bh + lh)–
2(lb)
= 2 (bh + hl)
= 2 (l+b) × h

23. VOLUME
Volume of a cuboid =
Length × Breadth × Height
Or
V = l × b × h
Where, V = volume
l = length, b = breadth
h = height

25. WHAT IS A RIGHT
CIRCULAR
CYLINDER ? A cylinder is a
right circular
cylinder if :
 Its base is a
circle and
 Radius of the
base is
perpendicular to
its height.

26. SURFACE AREA
 C.S.A. of
cylinder
= Area of
rectangular
sheet
= 2πrh
o T.S.A. of cylinder
= C.S.A. + Lid
area + Base
area
2

27. VOLUME
 Volume of a cylinder
= Area of base ×
height
= πr2h

29. WHAT IS A RIGHT
CIRCULAR CONE?
 In a right circular
cone, the radius
of the circular
base is
perpendicular to
its height.
 Also, Slant
Height
l =
Height h
Base
r
Slant Height
l

30. CURVED SURFACE
AREA
l l
2πr
r
Area of sector = Circumference of arc
Area of circle Circumference of circle
Area of sector = 2πr × πl 2 = πrl
2πl
C.S.A. of cone = Area of sector = πrl

31. TOTAL SURFACE
AREA
 T.S. A. of Cone = C.S.A. + Base
Area
= πrl + πr2
= πr (l +r)
2
B r
r

32. VOLUME
 Volume of Cone
= 1 × Volume of
Cylinder
3
= 1 × πr2h
3

34. SURFACE
AREA AND
VOLUMESurface area of sphere = 4
πr2
Volume of sphere = 4 πr3
3

36. SURFACE
AREA AND
VOLUME C.S.A. of hemisphere = 2πr2
 T.S.A. of hemisphere = C.S.A. + Base
Area
= 2πr2 + πr2
= 3πr2
 Volume of hemisphere = 2 πr3
3