**IX Chapter - 13 :**

**Surface areas and Volumes**

1. A solid cylinder has
a total surface area of 231cm2. Its curved surface area is 2/3 of the total
surface area. Find the volume of the cylinder.

Ans: 269.5cm2

2. The diameter of a
garden roller is 1.4m and it is 2m long. How much area will it cover in 5
revolutions?

Ans: 44m2

3. Three metal cubes
whose edge measure 3cm, 4cm and 5cm respectively are melted to form a single
cube, find its edge.

Ans: 6cm

4. The dimensions of a
cubiod are in the ratio of 1 : 2 : 3 and its total surface area is 88m2. Find
the dimensions.

Ans: 2, 4, 6 cm

5. Find the lateral
curved surface area of a cylindrical petrol storage tank that is 4.2m in
diameter and 4.5m high. How much steel was actually used, if 1/12 of steel actually used was wasted in making
the closed tank.

Ans: 59.4m2, 95.04m2

6. The radius and height of a cone are in the ratio 4 : 3. The area of the base is 154cm2. Find the area of the curved surface.

Ans: 192.5cm2

7. A sphere, cylinder and cone are of the same
radius and same height. Find the ratio of their curved surfaces.

Ans: 4 : 4 : √5

8. A hemispherical bowl of internal diameter 36cm
contains a liquid. This liquid is to be filled in cylindrical bottles of radius
3cm and height 6cm. How many bottles are required to empty the bowl?

Ans: 72

9. A hemisphere of lead
of radius 8cm is cast into a right circular cone of base radius 6cm. Determine
the height of the cone.

Ans: 28.44

Q.19. Find the volume
of the largest right circular cone that can be fitted in a cube whose edge is
14cm.

Ans: 718.66cm3

10. A well with 10m
inside diameter is dug 14m deep. Earth taken out of it is spread all around to
a width of 5m to form an embankment. Find the height of embankment.

Ans:4.66m

11. A metallic sheet is
of the rectangular shape with dimensions 48cm X 36cm. From each one of its
corners, a square of 8cm is cutoff. An open box is made of the remaining sheet.
Find the volume of the box.

Ans: 5120cm3

12. Water in a canal, 30dm wide and 12dm deep is flowing with
a velocity of 20km per hour. How much area will it irrigate in 30min. if 9cm of
standing water is desired? (10dm = 1 meter)

Ans: 4,00,000m2

13. Three cubes of each side 4cm are joining end to end. Find
the surface area of resulting cuboid.

Ans: 224 cm2

14. A hollow cylindrical pipe is 210cm long. Its outer and
inner diameters are 10cm and 6cm respectively. Find the volume of the copper
used in making the pipe.

Ans: 10560cm3

15. A semi circular sheet of metal of diameter 28cm is bent
into an open conical cup. Find the depth and capacity of cup.

Ans: 12.12cm, 622.26cm3

16. If the radius of a sphere is doubled, what is
the ratio of the volume of the first sphere to that of second sphere?

Ans: 1:8

17. The sum of length, breadth and height of a
cuboid is 21 cm and the length of its diagonal is 12 cm. Find
the surface area of the cuboid.

Ans: 297 cm2

18. The internal and
external diameters of a hollow hemispherical vessel are 20 cm and 28 cm
respectively. Find the cost of painting the vessel all over at 15 paisa per cm2

Ans: Rs. 324.34

19. A well of diameter
3m is dug 14 m deep. The earth taken out of it has been spread evenly all
around it to a width of 4 m to form an embankment. Find the height of the
embankment

Ans: 1.125 m

20. A right triangle
ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the
volume of the solid so obtained? Ans: 314
cm3

9th Surface Area and volume CBSE Test Paper-1

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9th Surface Area and volume CBSE Test Paper-2

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9th Surface Area and volume CBSE Test Paper-3

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9th Surface Area and volume CBSE Test Paper-1

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9th Surface Area and volume CBSE Test Paper-2

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9th Surface Area and volume CBSE Test Paper-3

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i need sums how does it came

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