Are you searching for Class 10 Maths Surface Areas and Volumes Important Questions for your CBSE board exam preparation?
Here is a high-quality, exam-oriented list of 35 questions taken from NCERT, NCERT Exemplar, and previous CBSE board papers.

These questions cover all major concepts including:

• Surface areas of 3D shapes
• Volumes of solids
• Volume conversion
• Water flow questions
• Packing and displacement questions
• Real-life application problems

Use them for board exam practice, school tests, and revision worksheets.

Class 10 Surface Areas and Volumes – Important Questions (Numbered 1 to 35)

(Questions are kept 100% original, exactly as provided)

1. A rectangular tank 15 m long and 11 m broad is required to receive the liquid contents from a full cylindrical tank of internal diameter 21 m and length 5 m. Find the least height of the tank that will serve the purpose.

2. A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?

3. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical ball of radius 9 cm is dropped into the tub and the level of the water is raised by 6.75 cm. Find the radius of the ball.

4. 500 persons have to dip in a rectangular tank which is 80 m long and 50 m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is 0.04 m²?

5. A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?

6. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical form of radius 9 cm is dropped into the tub and thus the level of water is raised by h cm. What is the value of h?

7. Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimension 16 cm × 8 cm × 8 cm when 16 spheres are packed and the box is filled with preservative liquid. Find the volume of this liquid. [Use π = 22/7]

8. A vessel in the shape of a cuboid contains some water. If three identical spheres each of radius 6 cm are immersed in water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 576 cm², find the radius of any of the spheres.

9. 150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of water in the vessel.

10. Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which 25\frac{2}{5}52​ of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant? [CBSE 2014]

11. 16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box. [NCERT EXEMPLAR]

12. Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in 10 minutes?

13. Water in a canal 1.5 m wide and 6 cm deep is flowing with a speed of 10 km/hr. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired? [NCERT EXEMPLAR]

14. A farmer runs a pipe of internal diameter 20 cm from the canal to irrigate his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled? [CBSE 2014, NCERT]

15. A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice. How much canvas cloth is required to cover the heap? [NCERT EXEMPLAR]

16. A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. [NCERT EXEMPLAR]

17. A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl? [NCERT EXEMPLAR]

18. A factory manufactures 120,000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at ₹0.05 per dm². [NCERT EXEMPLAR]

19. The 34\frac{3}{4}43​th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel. [CBSE 2017]

20. A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3 m and its height is 3.5 m? [Use π = 22/7]

21. Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank. The radius of the base is 40 cm. If the increase in the level of water in the tank in half an hour is 3.5 m, find the internal diameter of the pipe. [CBSE 2015]

22. Water flows at the rate of 15 km/hr through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

23. A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired? [NCERT EXEMPLAR]

24. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm², find the volume of cylinder. [Use π = 22/7] [CBSE 2016]

25. A tent of height 77 dm is in the form a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at ₹3.50 per m². [Use π = 22/7] [CBSE 2014]

26. The largest sphere is to be curved out of a right circular cylinder of radius 7 cm and height 18 cm. Find the volume of the sphere.

27. A triangular triangle whose sides are 3 cm, 4 cm and 5 cm is revolved about the sides containing the right angle in two ways, forming two cones. Find their curved surfaces.

28. A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of ₹25 per metre. [Use π = 22/7] [CBSE 2014]

29. The volume of a hemisphere is 2425122425 \frac{1}{2}242521​ cm³. Find its curved surface area. (Use π = 22/7)

30. The difference between the outer and inner curved surface areas of a hollow right circular cylinder 14 cm long is 88 cm². If the volume of metal used in making the cylinder is 176 cm³, find the outer and inner diameters of the cylinder. [CBSE 2001]

31. The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm² of the surface is 10 paise. Find the total cost to paint the vessel all over.

32. Prove that the surface area of a sphere is equal to the curved surface area of the circumscribed cylinder.

33. If the total surface area of a solid hemisphere is 462 cm², find its volume. (Take π = 22/7)

34. Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm? [NCERT EXEMPLAR]

35. A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. The volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

These 35 most important questions of Surface Areas and Volumes Class 10 will help you score better in school exams, periodic tests, pre-boards, and CBSE board exams.
Practice them regularly and try writing complete steps as required by CBSE.