CBSE Class 9 Surface Areas and Volumes Sure Shot Questions

Read and download the CBSE Class 9 Surface Areas and Volumes Sure Shot Questions. Designed for 2026-27, this advanced study material provides Class 9 Mathematics students with detailed revision notes, sure-shot questions, and detailed answers. Prepared by expert teachers and they follow the latest CBSE, NCERT, and KVS guidelines to ensure you get best scores.

Advanced Study Material for Class 9 Mathematics Chapter 13 Surface Areas and Volumes

To achieve a high score in Mathematics, students must go beyond standard textbooks. This Class 9 Chapter 13 Surface Areas and Volumes study material includes conceptual summaries and solved practice questions to improve you understanding.

Class 9 Mathematics Chapter 13 Surface Areas and Volumes Notes and Questions

 

CBSE Class 9 Surface Areas and Volumes Sure Shot Questions. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

11. The dimensions of a prayer Hall are 20m x 15m x 8m. Find the cost of painting its walls at Rs. 10 per m2.

12. Find the curved surface area of a right circular cylinder whose height is 13.5 cm and radius of tis base is 7 cm. Find also its surface area.

13. The exterior diameter of an iron pipe is 25cm and it is one cm thick. Find the whole surface are of the pipe it is 21cm long.

14. A roller 150 cm long has a diameter of 70 cm. To level a playground it takes 750 complete revolutions. Determine the cost of leveling the playground at the rate of 75 paise per m2.

15. Find the total surface area of a cone, if its slant height is 21 cm and the diameter of its base is 24 cm.

16. The volume of a sphere is 4851 cm3. How much should its radius be reduced so that it volume becomes 4312/3 cm3.

17. A river, 3 m deep and 40m wide, is flowing at the rate of 2km/hr. How much water will fall into the sea in a minute?

18. Find the capacity in litres of a conical vessel whose diameter is 14 cm and slant height is 25 cm.

19. What is the total surface area of a hemisphere of base radius 7cm?

20. A village having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20m x 15m x 6m. For how many days, the water of the tank will be sufficient for the village?

21. Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cmrespectively how many square sheets of paper of side 40 cm would she require?

22. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the tiles is Rs 360 per dozen.

23. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all the 12 edges?

24. Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm. For all the overlaps, 5% of the total surface area isrequired extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind.

25. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions
4 m × 3 m?
 
26. Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use 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 25 cm with a 3.5 cm radius?
 
27. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm. Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
 CBSE Class 9 Surface Areas and Volumes Sure Shot Questions
28. Find (i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high. (ii) how much steel was actually used, if 1/12 of the steel actually used was wasted in making the tank.
 
29. Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.
 
30. The height of a cone is 16 cm and its base radius is 12 cm. Find the curved surface area and the total surface area of the cone (Use π= 3.14).
 
31. A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length (height) as 20 cm. If each 1 cm2 of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob.
 
32. In the adjoining figure you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
CBSE Class 9 Surface Areas and Volumes Sure Shot Questions 
33. A conical tent is 10 m high and the radius of its base is 24 m. Find (i) slant height of the tent. (ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
 
34. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π= 3.14).
 
35. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2.
 
36. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.
 
37. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs 5 per 100 cm2.
 
38. A right circular cylinder just encloses a sphere of radius r. Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in (i) and (ii).
 CBSE Class 9 Surface Areas and Volumes Sure Shot Questions
39. A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
 
40. A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required?
 
41. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
 
42. A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.
 
43. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
 
44. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
 
45. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?
 
46. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
 
47. The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such.
 
48. Monica has a piece of canvas whose area is 551 m-. She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with it.
 
49. 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.
 
50. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
 
51. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square metre, find the (i) inside surface area of the dome, (ii) volume of the air inside the dome.
 
52. Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the (i) radius r’of the new sphere, (ii) ratio of S and S’.
 
53. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?
 
54. The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and the volume of the cone (taking π= 22 /7)
 
55. The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1% approximately.
 
56. Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π= 3.14]
 
57. A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3. If the present depth of water is 1.3 m, find the volume of water already used from the tank.
 
58. Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.
 
59. How many square metres of canvas is required for a conical tent whose height is 3.5 m and the radius of the base is 12 m?
 
60. Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.
 
61. A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, find how many litres of milk is needed to serve 1600 students.
 
62. A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m2. How many revolutions did it make?
 
63. A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement 40 m × 25 m × 15 m. For how many days will the water of this tank last?
 
64. A shopkeeper has one spherical laddoo of radius 5cm. With the same amount of material, how many laddoos of radius 2.5 cm can be made?
 
65. A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the volume and the curved surface of the solid so formed.
 
66. Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if the rain fall is 1 cm. Give your answer to the nearest integer. (Take π= 3.14)
 
67. A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube ?
 
68. A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.
 
69. A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m
 
(i) How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?
 
(ii) Find the volume of the cone.
 
70. The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.
 
71. The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.
 
72. A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.
 
73. A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height ?
 
74. 30 circular plates, each of radius 14 cm and thickness 3cm are placed one above the another to form a cylindrical solid. Find : (i) the total surface area (ii) volume of the cylinder so formed.
 
75. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
 

Please click the link below to download CBSE Class 9 Surface Areas and Volumes Sure Shot Questions.

Chapter 01 Number Systems
CBSE Class 9 Number Systems Sure Shot Questions
Chapter 02 Polynomials
CBSE Class 9 Polynomials Sure Shot Questions
Chapter 03 Coordinate Geometry
CBSE Class 9 Coordinate Geometry Sure Shot Questions
Chapter 04 Linear Equations In Two Variables
CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
Chapter 05 Introduction to Euclids Geometry
CBSE Class 9 Introduction to Euclids Geometry Sure Shot Questions
Chapter 06 Lines and Angles
CBSE Class 9 Lines and Angles Sure Shot Questions
Chapter 07 Triangles
CBSE Class 9 Triangles Sure Shot Questions
Chapter 08 Quadrilaterals
CBSE Class 9 Quadrilaterals Sure Shot Questions
Chapter 09 Areas of Parallelograms and Triangles
CBSE Class 9 Areas of Parallelogram and Triangle Sure Shot Questions
Chapter 10 Circles
CBSE Class 9 Circles Sure Shot Questions
Chapter 11 Constructions
CBSE Class 9 Constructions Sure Shot Questions
Chapter 12 Herons Formula
CBSE Class 9 Herons Formula Sure Shot Questions
Chapter 13 Surface Areas and Volumes
CBSE Class 9 Surface Areas and Volumes Sure Shot Questions
Chapter 14 Statistics
CBSE Class 9 Statistics Sure Shot Questions
Chapter 15 Probability
CBSE Class 9 Probability Sure Shot Questions

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CBSE Class 9 Mathematics Chapter 13 Surface Areas and Volumes Study Material

Students can find all the important study material for Chapter 13 Surface Areas and Volumes on this page. This collection includes detailed notes, Mind Maps for quick revision, and Sure Shot Questions that will come in your CBSE exams. This material has been strictly prepared on the latest 2026 syllabus for Class 9 Mathematics. Our expert teachers always suggest you to use these tools daily to make your learning easier and faster.

Chapter 13 Surface Areas and Volumes Expert Notes & Solved Exam Questions

Our teachers have used the latest official NCERT book for Class 9 Mathematics to prepare these study material. We have included previous year examination questions and also step-by-step solutions to help you understand the marking scheme too. After reading the above chapter notes and solved questions also solve the practice problems and then compare your work with our NCERT solutions for Class 9 Mathematics.

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Our advanced study package for Chapter Chapter 13 Surface Areas and Volumes includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 9 students learn as per syllabus for 2026 exams.

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Yes, our subject matter experts have updated the Chapter Chapter 13 Surface Areas and Volumes material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.