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NCERT Class 9 Mathematics Surface Area and Volume Formative Board Sample Problems
Assessment
Fill in the blank
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________ () ⟋ ()
Solution
(a) Remain same
So if r is doubled, h is halved, CSA will remain same
(b) 616 cm2 Surface area
(c)
(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 12 cm radius
(c) Radius of the cone is doubled and height is halved, the volume will be halved
(d) A river 10 m deep and 40 m wide is flowing at the rate of 2 m 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
Solution
(a) True. All of them will have height as r as hemisphere height can be r only.
For cylinder
Hemisphere
Cone
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 10 m, 40 m, 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 9 m respectively. Find the area of our walls of room?
(a)
(b)
(c)
(d)
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
(a)
(b)
(c)
(d)
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 7 cm
(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 30 cm with a 2.7 cm radius? (Use p = 2217)
(a)
(b)
(c)
(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)
Volume
Question 8
Find the maximum length of the rod that can be kept in cuboidal box of sides 30 cm, 20 cm and
10 cm.
(a)
(b)
(c)
(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) 32 cm
(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
(a)
(b)
(c)
(d) None of the above
Solution (c)
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 |