Maths project surface area and volume_by_chirag_jain_ix_a_roll no 17

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THE
PRESENTATIO
N BEGINS

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

 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.

 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.

 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.

SURFACESURFACE
AREAAREA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

VOLUMEVOLUME
 Volume of a
cube of edge
a units is a3
cubic units.

TOTAL SURFACETOTAL SURFACE
AREAAREA 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

LATERAL SURFACELATERAL SURFACE
AREAAREA
 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

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

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

SURFACE AREASURFACE AREA
 C.S.A. of cylinder
= Area of
rectangular sheet
= 2πrh
o T.S.A. of cylinder
= C.S.A. + Lid area
+ Base area
= 2πrh + πr2
+ πr2
= 2πr (h+r)

VOLUMEVOLUME
 Volume of a cylinder
= Area of base ×
height
= πr2
h

WHAT IS A RIGHTWHAT IS A RIGHT
CIRCULAR CONE?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

CURVED SURFACECURVED SURFACE
AREAAREA
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

TOTAL SURFACETOTAL SURFACE
AREAAREA
 T.S. A. of Cone = C.S.A. + Base Area
= πrl + πr2
= πr (l +r)
l
2
B rπ=
r

VOLUMEVOLUME
 Volume of Cone
= 1 × Volume of Cylinder
3
= 1 × πr2
h
3

AND VOLUMEAND VOLUME
 Surface area of sphere = 4 πr2
 Volume of sphere = 4 πr3
3

AND VOLUMEAND 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

Maths project surface area and volume_by_chirag_jain_ix_a_roll no 17

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Maths project surface area and volume_by_chirag_jain_ix_a_roll no 17