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WELCOME

- WELCOME

Surface Areas and Volumes

By

N.Vinay Chowdary IX- 'A'

Surface Area of a Cuboid

D

C

A

B

h

l

H

G

b

E

F

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

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

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

Questions Answers

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)

Q. 2 The diameter of a sphere is decreased by

50. What is the ratio between initial and final

curved surface areas?

- Ans

Q. 3 Find the volume of the largest right

circular cone that can be fitted in a cube whose

edge is 14cm?

- Ans

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

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

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

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

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

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

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

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)

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

Q. 13 If two circular cylinders of equal volume

have their height in the ratio 14, find the

ratio of their radii?

- Ans

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

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

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

THANKS

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