volume and surface area class ix

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Surface Areas and Volumes
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Polyhedron
Examples of Polyhedra    

• A polyhedron is a solid with flat faces(from
  Greek poly- meaning "many" and -hedron meaning
  "face"). Each face is a polygon (a flat shape
  with straight sides).

Can you guess the special name for cube and
cuboid? ( Based on number of faces?
we can call cube and cuboid as hexahedron
because it has 6 faces
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Surface area and Volume of Cube and Cuboid
4
Cube
A cube has 6 congruent square faces
 
 
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A cuboid has 6 faces.
To find the surface area of a cuboid, we
calculate the total area of all of the faces.
The top and the bottom of the cuboid have the
same area.
The front and the back of the cuboid have the
same area.
. The side faces of the cuboid have the same area
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Surface area of a cuboid
 
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. Exercise 13.1.5 A cubical box has each edge
10 cm and another cuboidal box is 12.5 cm long,
10 cm wide and 8 cm high. (i) Which box has the
greater lateral surface area and by how much?
Cube side a 10 cm LSA ?????????? ???? ?????? ???????? ?? ?? ?? ???? ?? ?? ???? ?? ???? ?? LSA ?????? ???? ?? -----(1) Cubiod l 12.5 cm b 10 cm h 8 cm LSA area of four faces 2lh 2bh sq.cm 2h(lb) sq.cm LSA ???? ????.?????? ???? ?? ????????.?? ???? ?? LSA ?????? ???? ?? -------(2)
From (1) and (2) area of cube is greater by
40 sq.cm
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Extra questionA cubical box has each edge 11
cm and another cuboidal box is 12cm long, 10 .5cm
wide and 8 cm high. Which box has the smaller
total surface area and by how much?
Cube side a 11 cm TSA 6???????? ???? ?????? ???????? 6 ?? ?? ???? ?? 6 ???? ?? ???? ?? LSA 726 ???? ?? -----(1) Cubiod l 12cm b 10.5 cm h 8 cm TSA area of four sides 2lh 2bh 2lb sq.cm 2 (lh lb bh) sq.cm TSA ?? ????.??????.????????????.?? ???? ?? ??(??????????????) ???? ?? TSA 2?????? ???? ?? TSA 612 ???? ?? -------(2)
Conclusion ??????
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If the perimeter of one face of a cube is 40
cm, find its lateral surface area

• Given 4a 40 cm
• ???10 ????
• Lateral surface area 4 ?? 2 ???? 2
• ??????????????? ?????????????? ????????4 10 2
  ???? 2
• ??????????????? ?????????????? ????????400
  ???? 2

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Area of the sheet required lateral surface
area area of the base
2 l h 2 b h l b sq.m
21.50.6521.250.651.51.25 ?? 2
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Shanti sweet stall was placing order for
cardboard boxes for packing sweets. They need two
types of boxes , one with dimension 25cm
X 20cm X 5 cm and another with dimesions 15 cm X
12 Cm x5cm. For all the overlaps, 5 of the toal
surface is required extra. If the cost of the
cardboard is Rs4 per 1000 sq.m, find the cost of
cardboard required for supplying 250 boxes of
each kind
For Type1 box L 25 cm B 20 cm H 5
cm No. of boxes 250
Area of the cardboard required for 1 box TSA
of the box 5 of TSA
 
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For Type 2 box l 15 cm b 12 cm h 5
cm No. of boxes 250
 
 
 
Given cost per 1000 sq. m Rs 4
Total cost Rs 105 100 250(??????1??????2)
4 1000
Ans Total cost Rs 2184
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The total surface area of a cube is 726 ???? 2
.Find the length of its edge.

• Total surface area 6 ?? 2 ???? 2
• ?6 ?? 2 726
• ? ?? 2 726 6 121
• ? ?? 2 11 2
• ???11
• ???h?? ??????????h ???? ?????? ????????11 ????

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Solid objects occupy space. The measure of this
occupied space is called as its Volume
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The capacity of an object is the volume of
substance its interior can accommodate
17
Volume of cube and Cubiod
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Exercise 13.5 .1
Here L 4 cm , W 2.5 cm , H 1.5 cm
Volume of 1 box LB H cub. unit
 
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Exercise 13.5 Q 3 A cuboidal vessel is 10 m
long and 8 m wide. How high must it be made to
hold 380 cubic meters of a liquid?
According to the question l 10 m b 8 m h
?? V 380 cub. m
V lbh cub. cm
 
 
 
The height of the vessel is 4.75 m
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A village, having a population of 4000, requires
150 litres of water per head per day. It has a
tank measuring 20 m 15 m 6 m. For how many
days will the water of this tank last?
Volume of the tank ????h20156 ?? 3
1800 ?? 3 -----(A)
Quantity of water required for 4000 people per
day 4000150 litres
Why?
Water required for 4000 people per day
4000150 1 1000 ?? 3
Water required for 4000 people per day 600 ??
3 -----(??)
No. of days water will last ????????????
???? ??h?? ???????? ???????????????? ????
?????????? ???????????????? ?????? ??????
180 0?? 3 600 ?? 3 3
22
A solid cube of side 12 cm is cut into eight
cubes of equal volume. What will be the side of
the new cube? Also, find the ratio between their
surface areas..
Given side of bigger cube is S 12 cm. Let
the side of a smaller cube a cm
 
 
? a 6
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ii. We have to find the ratio of surface areas
of two cubes
 
 
4 1
The ratio of the surface area of the given cube
to that of smaller cube is 4 1
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A river 3 m deep and 40 m wide is flowing at the
rate of 2 km per hour. How much water will fall
into the sea in a minute?
Rate of flowing of water in 1 hour 2 km
i. e. Rate of flowing of water in 60 mins 2
km 2000 m
Note For that 1 hour, the water is flowing
like a cuboid whose length distance to which
the water flows in 1 hr, and depth and width
remaining what is given
 
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Extra QuestionThe volume of a cuboidal box is
10368 cu.cm. If its dimensions are in the ratio
3 2 1, find its lateral surface area.
Let ??3?? ????, ??2?? ???? ?????? h
1 ?? ????
?????????? ??10368 ???? 3
According to question , (3??) 2?? ????
10338
Find k., then find length, breadth and height
26
A godown measures 40 m 25 m 10 m. Find the
maximum number of wooden crates each measuring
1.5 m 1.25 m 0.5 m that can be stored in the
godown.
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