Transcript SURFACE AREAS AND VOLUMES - Digital Equalizer

CUBE
CYLINDER
Formulas 1.Area of cuboid =
2[lb+bh+hl]
2.Volume of cuboid = l*b*h .
3.Later`al surface area of
cuboid =2(l+b) h
H
B
L
Cuboid is rectangular
closed curve which
has 12 edges ,6 faces
and 8 vertices is
called cuboid .
Example of area of cuboid :-
Q1 . Three cubes each of side 5cm are joined
end to end .Find the surface area of the
resulting cuboid ?
Sol :5cm
5cm
5cm
5cm
5cm
l =Length ,b=Breadth and
,h=Height .
l=15cm ,b=5cm and ,h=5cm .
Surface area of the cuboid =
2[lb+bh+hl ] cm²
= 2[15*5 +5*5 +15*5 ] cm²
= 2[75 +25 +75 ] cm²
=2[175 ] cm²
=350 cm² .
Example of volume of cuboid :Q2 . Two cubes each of volume 64
cm² are joined end to end . Find
the volume of the resulting cuboid .
Sol :4cm
4cm
4cm
4cm
Let the length of each edge of the
cube of volume 64 cm² be xcm .
*Then ,
Volume = 64 cm³
= x³ =64
= x = ³√64
= x = 4 cm .
l=Length =(4 + 4 ) cm = 8cm .
b=breadth = 4cm . And
h=height =4cm .
*Volume of the cuboid
*
=8×4×4
*
=128 cm³.
= l×b×h
Example of Lateral surface area of cuboid
Q3 . A room has length 4m , breadth 2.5
m and height 3m . Find the lateral surface
area of four walls .
Sol :- l=Length =4m ,
b=Breadth =2.5m,
h=Height =3m .
lateral surface area = 2(l+b) h
=2(4+2.5) 3
*
*
*
= 2(6.5) 3
= 13.0 ×3
= 39.0 m².
*Formulas of cube :*1. Surface area of cube=6a²
*2. Volume of cube=a³
*3. lateral surface area of
cube = 4a²
*
*
CUBE
L
L
L
Cube is squarical of
figure which has length
,breadth and height are
equal and have 6 faces ,8
vertices and 12 edges .
*Example of Surface area
*Of cube :*Q1. A cubical box has
each edge 1.25m . Find
the Surface area of
cube.
*Sol
:- a=edge=1.25m
Surface area of cube
=6a²
=6(1.25)²
=6× 1.5625
=9.3750m².
*Example of Volume of cube :*Q2. A child playing with building blocks
,which are of the shape of cubes ,has built
a structure . If the edge of each cube is
3cm , find the volume of the structure
built by the child .
Volume of each cube
=edge×edge×edge
= 3×3×3cm³
= 27cm³
Number of cubes in the structure
=15
Therefore ,Volume of the structure
=27×15cm³
=405cm³
*Example of lateral surface
area of cube :-
*Q3. Edge of cube 7.5cm. Find
the lateral Surface area of
cube.
*Sol :- a=Edge =7.5cm
* Lateral surface area of cube=4a²
*
=4(7.5)²
*
=4×56.25
*
=225.0cm²
Formulas of cylinder :1. Curved surface area of a
cylinder =2𝜋rh
2. Total surface area of a
cylinder =2𝜋r(r+h).
3.Volume of cylinder =𝜋r²h.
*
*
*Circular
CYLINDER
h
r
shape of an object
which have a height are called
Cylinder.
*Example
of curved surface area
of Cylinder:*Q1. Savitri had to make a modal
of a cylindrical kaleidoscope for
her science project .She wanted
to use chart paper to make the
curved surface of the
kaleidoscope. What would be the
area of chart paper reqired by
her ,if she wanted to make a
kaleidoscope of length 25cm
with a 3.5cm radius ?
SOL:-
h
r
Radius of the base of the Cylindrical
kaleidoscope(r)=3.5cm
*Height (length) of kaleidoscope
*
(h)=25cm.
*Area of chart paper required =curved
surface area of the kaleidoscope
*
=2𝜋rh
*
=2×22/7×3.5×25cm²
*
=550cm²
*Example of Total surface area of
a cylinder :-
*Q2. In a hot water heating
system ,there is a cylindrical pipe
Of length 28m and diameter 5m.
Find the total radiating surface in
the system.
*Sol:- l =Length =28m
*d =Diameter =5m
* r=Radius =5/2 = 2.5m
* Total surface area of a cylinder
*
=2𝜋r(r+h)
*
=2×22/7×2.5(2.5+28)
*
=110.0/7×(30.5)
*
= 3355.0/7
*
= 479.29cm².
*
*Example of Volume of cylinder :*Q3 . The pillars of a temple are
cylindrically shaped . If each pillar has
*a circular base of radius 20cm and
height 10m ,How much concrete
mixture would be required to build
14 such pillars ?
20cm
1000cm
Sol:Radius of base of a cylinder =20cm
Height of the cylindrical pillar = 10m=
= 1000cm
So, Volume of each cylinder=𝜋𝑟²ℎ
=22/7×20×20×1000cm³
=8800000/7cm³
* 8.8/7m³(Since 1000000cm³=1m³ )
*Therefore, volume of 14pillars =
volume of each cylinder ×14
*
=8.8/7×14m³
*
=17.6m³
*So, 14 pillars would need 17.6m³ of
concrete mixture.
*=
*Ishani Sarvodaya kanya Vidiyala
*Student Name:- Neha, Nisha,
*Class :- 10th E
*Teacher Name:- Indu Bhardwaj., Sunil
Kumar
*Topic :- Surface area and Volumes.