Surface Areas and Volumes

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WELCOME

• WELCOME

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Surface Areas and Volumes

By
N.Vinay Chowdary IX- 'A'
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Surface Area of a Cuboid
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A
B
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l
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b
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The surface of a cuboid consists of six
rectangular faces. So, the surface area of a
cuboid equals the sum of the areas of its six
rectangular faces. Procedure to derive the
formula for the surface area of a cuboid is as
follows
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Procedure

• Consider a cuboid whose length is l cm, breadth b
  cm and height h cm as shown in the above figure.
• Area of face ABCD Area of face EFGH (l x b)
  cm2.
• Area of face AEHD Area of face BFGC (b x h)
  cm2.
• Area of face ABFE Area of face DHGC (l x h)
  cm2.
• Therefore, total surface area of the cuboid Sum
  of the areas of all its six faces
• 2(l x b) 2(b x h) 2(l x h) cm2
• 2(l x b b x h l x h) cm2
• 2(lb bh lh) cm2
• 2(length x
  breadth breadth x height length x height) cm2

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Surface Area of a Cube

• Since all the six faces of a cube are
  squares of the same size i.e. for a cube we have
  lbh. Thus, if 1 cm is the length of the edge or
  side or a cube, then
• Surface area of the cube 2(l x l l x l
  l x l)
• 2 x 3l2 6l2 6(Edge)2

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Questions Answers
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Q. 1 Three equal cubs are placed adjacently in a
row. Find the ratio of total surface area of the
new cuboids to that of sum of the surface areas
of the three cubes?
(Ans)                                        
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Q. 2 The diameter of a sphere is decreased by
50. What is the ratio between initial and final
curved surface areas?

• Ans

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Q. 3 Find the volume of the largest right
circular cone that can be fitted in a cube whose
edge is 14cm?

• Ans

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Q. 4 A plastic box 1.25 m long,1.05 m wide and
75cm deep is to be made. It is to be open at the
top. Ignoring the thickness of the plastic sheet,
determine the area of the sheet required for
making the box and also find the cost of sheet
for it, if a sheet measuring 1sq.m. cost Rs. 20 ?

• Ans

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Q. 5 A reservoir is in the form of rectangular
parallelepiped. Its length is 20 m . If 18kl of
water is removed from the reservoir, the water
level goes down by 15cm. Find the width of the
reservoir?

• Ans

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Q. 6 How many litres of water flow out of a
pipe having an area of cross-section of 5 Sq. cm.
in one minute if the speed of the water in the
pipe is 30cm/sec?

• Ans

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Q. 7 An open box is made of wood 3cm thick. Its
external length, breadth and height are
1.48m,1.16m and 8.3dm. Find the cost of painting
the inner surface of Rs. 50 per sq metre?

• Ans

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Q. 8 A wood toy is in the form of a cone
surmounted on a hemisphere. The diameter of the
base of the cone is 6cm and its height is 4cm.
Find the cost of painting the toy at the rate of
Rs. 5 per 1000 sq.cm ?

• Ans

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Q. 9 A pendulum swings through an angle of 30
degree and describes an arc of length 7.7cm. Find
the length of the pendulum?

• Ans

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Q. 10 Find the length of the arc, the area of
the sector of a circle and the area of segment of
the circle, if the radius of the circle is 28cm
and the angle of the sector is 60 degree?

• Ans

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Q. 11 The semi-circular sheet of metal of
diameter 28cm is bent into an open conical cup.
Find the depth and the capacity of cup?

• Ans

To calculate the depth of cone sqrt(h2-r2)
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Q. 12 If V is the volume of a cuboid of
dimension a,b,c and S is its surface area, then
prove that

• Ans

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Q. 13 If two circular cylinders of equal volume
have their height in the ratio 14, find the
ratio of their radii?

• Ans

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Q. 14 A circular tent is cylindrical to a
height of 3 metres and conical above it. If its
diameter is 105m and the slant height of the
conical portion is 53m, calculate the length of
canvas 5m wide to make the required tent?

• Ans

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Q. 15 A wall of the length 10m was to be built
across an open ground. The height of the wall is
4 m and thickness of the wall is 24cm. If this
wall is to be built up with bricks whose
dimensions are 24cmx12cmx8cm, how many bricks
would be required?

• Ans

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Q. 16 Three metal cubes whose edges measure
3cm,4cm and 5cm respectively are melted to form a
single cube. Find the edge of the new cube. Also
find the surface area?

• Ans

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THANKS