NCERT Class 9 Mathematics Surface Area and Volume Formative Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 1

(a) A cylinder radius is doubled and height is halved, the curved surface area of the cylinder will________ (Increase/decrease/remain same)

(b) The radius of the sphere is 7 cm, the surface area of the sphere is ________ (/7 /)

(c) Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a big cube.

The volume of the big cube is________ (/)

(d) The total surface area of a hemisphere of radius 10 cm using value of is________ () / ()

(e) A right circular cylinder just encloses a sphere of radius. The ratio of their surface area is________ (1: 1/1: 2)

(f) The lateral surface area of a cube is 256 m2, the volume is________ () / ()


(a) Remain same

So if r is doubled, h is halved, CSA will remain same

(b) 616 cm2 Surface area


(d) 956 cm2 Total surface area =

(e) 1: 1 In this height of cylinder will be 2r and radius of cylinder wiH r. So it is equal

(f) Lateral surface area and Volume

True or False statement

Question 2

a) A cylinder, hemisphere and cone stand on equal base and same height, the Volume ratio is 3: 2: 1

b) The radius of a solid sphere is 24 cm. 8 spheres can be made from it of 12cm radius

c) Radius of the cone is doubled and height is halved, the volume will be halved

d) A river 10m deep and 40m wide is flowing at the rate of 2m per min. Water will flow into the sea from river

e) A cylinder radius is halved and height is doubled, the volume will become halved

f) The side of the cube is 4 cm, the diagonal length is cm


a) True. All of them will have height as r as hemisphere height can be r only.

For cylinder



So ratio is 3: 2: 1

b) True Sphere volume

c) False. Volume will be doubled Volume is given by

d) True. It is equal to the volume of the cuboid 10m, 40m, and 120 m

e) True.

b) False

Multiple choice Questions

Question 2

The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of our walls of room?





Solution (b)

Area of the walls is given by

Question 3

The plastic paint in a Asian paint container is sufficient to paint an area equal to How many blocks of dimensions can be painted out of this container





Solution (d)

Total surface area of one block

Let n blocks can be painted out by the paint of the container.

Area of n bricks

Area that can be painted by the paint of the container

n = 1000

Therefore, 100 blocks can be painted out by the paint of the container

Question 5

Curved surface area of a cone is and its slant height is 14 cm.

a) Radius of the cone is 7cm

b) Total surface area is

c) Height of the cone is v147

d) None of the above

Solution (a) , (b) , (c)

Curved surface area =

So r = 7 cm

Now total surface area

Question 6

Sita had to make a model of cylindrical kaleidoscope for her science project. She wanted to use black chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 30cm with a 2.7 cm radius? (Use p = 2217)




d) None of these

Solution a

Curved surface of cylinder = 2urh

Question 7

The radii of two cones are in the ratio of 2: 3 and their heights are in the ratio of 7: 3. The ratio of their volumes is

a) 20: 9

b) 28: 9

c) 29: 29

d) None of these

Solution (c)


Question 8

Find the maximum length of the rod that can be kept in cuboidal box of sides 30cm, 20cm and





d) None of these

Solution (a)

Diagonal is the longest length in the cuboid so

Question 9

A box is made entirely of glass panes (including base) held together with tape. It is 3 cm long, 2.5 cm wide and 2.5 cm high. How much of tape is needed for all the 12 edges?

a) 30 cm

b) 32cm

c) 40 cm

d) None of these

Solution (b)

Length of tape

Question 10

The curved surface area of a right circular cylinder of height 14 cm is . Find the Volume of the cylinder. Assume




d) None of the above

Solution (c)

Match the column

Match the Column
Curved surface area of Cone
Curved surface of Hemisphere
Curved surface area of Cylinder
Total surface area of Hemisphere
Total surface area of cone