CBSE I NCERT I IX SURFACE AREAS AND VOLUMES

CBSE I NCERT I  IX SURFACE AREAS AND VOLUMES

Surface Area of a Cuboid and a Cube          Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone        Surface Area of a Sphere
Volume of a Cuboid                                       Volume of a Cylinder  
Volume of a Right Circular Cone                 Volume of a Sphere

   Set Paper-1                                                 Section A

1.         The curved surface area of a right circular cylinder of height 14 cm is 88cm2. Find the diameter of the base of the cylinder. 

2.        Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base of the cylinder is 0.7m, find its height. 

3.        Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find    (i) the curved surface area and  (ii) the total surface area of a hemisphere of radius 21 cm. 

4.        The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. 

5.        Find the radius of a sphere whose surface area is 154cm2. 

6.        A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a packet containing 12 such boxes? 

7.        A cubical water tank is 6m long, 5m wide and 4.5m deep. How many liters of water can it hold? 

8.        The capacity of a cubical tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.3m and 10m. 

9.        The height and the slant height of a cone are 21cm and 28 cm respectively. Find the volume of the cone. 

10.      If the volume of a right circular cone of height 9cm is 48π cm3, find the radius of the base. (Use π=3.14)

11.        A triangle ABC with sides 5cm, 12cm and 13cm cm is revolved about the side 12 cm. Find the volume of the solid so obtained. 

12.      Find the volume of a sphere whose surface area is 154cm2. 

13.      How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold? 

14.      Find the amount of the water displaced by a solid spherical ball of diameter (i) 28cm (ii) 0.21m 

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

Section B

16.      A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm3) is needed to fill this capsule? 

17.      A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank. 

18.      The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3? 

19.      A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kilolitres? 

20.     The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28cm, find  (i) height of the cone (ii) Slant height of the cone. (iii) Curved surface area of the cone. 

21.      A heap of the wheat is the form of a cone whose diameter is 10.5m and height is 3m. Find its volume. The heap is to be covered by congas to protect it from rain. Find the area of the canvas required. 

22.     The circumference of the base of a cylindrical vessel is 132 cm and height is 25 cm. How many liters of water can it hold? 

23.     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.\ 

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

25.     A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm. Find the ratio of their surface areas. 

26.     A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50per m2. 

27.     The floor of a rectangular hall has a perimeter 250m If the cost of painting the four walls at the rate of Rs 10per m2 is Rs 15000, find the height of the hall. 

Section C

28.     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 titles is Rs 360 per dozen. 

29.     A plastics box 1.5 m long wide and 65 cm deep is to made. It is opened at the top. Ignoring the thickness of the plastics sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of the sheet for it, if a sheet measuring the box. 

30.     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 12 edges? 

31.      Savitri had to make a model of 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 25cm with a 2.5 cm radius? (Use π=22/7) 

32.     A metal pipe is 77 cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4 cm. Find its        (i) inner curved surface area.      (ii) Outer curved surface area. (iii) Total surface area. 

33.     In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. 

34.     The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding. 

35.     A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6m, find the cost of painting it, given the cost of painting is Rs 5 per 100cm2. 

Test Paper -2     Questions Bank
1. An underground water tank is in the shape of cube of side 7 m. What will be its volume?
2. What will be volume of a box whose length 16 m, breadth 8 m and height is 5 m?
3. The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of  our walls of room?
4. The volume of a cube is 27a3 . Find the length of its edge?
5. How much Aluminium sheet will be required to make a container with lid whose length is 13 m, breadth is 8 m and height is 4 m?
6. The volume of a cube is 1331 cm3 . Find the length of its edge?
7. The length of diagonal of a cube is 17.32 cm. Find the volume of that cube?
8. Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a cube. Find the volume of that cube?
9. Two cubes have edge 10 m. Their edges have been joined and form a cuboid. What will be the surface area of cuboid thus formed?
10. The total volume of a cube is 512 cubic cm. Find the side of a cube?

11. A rectangular box 14 cm long, 10 cm wide and 5 cm high is to be made with card-board. Find the area of card-board to make that box?
12. What will be the volume of a cylindrical tank whose radius is 7 cm and height is 5 cm?
13. How many solid spheres of  2/3 cm radius can be made from a solid sphere of 2 cm radius?
14. If the volume and surface area of a sphere is numerically same then what will be its radius?
15. The volume of a right circular cylinder is 392 π cm3 and its height is 8 cm. Find the radius?
16. The surface area of a sphere is 448 p  cm2 . Find its radius?
 17. What will be the edge of a cube? If its surface area is 324 sq cm .
 18. The volume of a hemisphere is 144 π cm³. What will be its radius?
19. The curved surface area of a cone is 140 π cm². What will be the radius of cone whose slant height is 5 cm.
20. The radius of a solid sphere is 12 cm. How many sphere can be made from it of 6cm radius?
21. The volume of a cuboid is 840 cm³. If its length is 14 cm and breadth is 5 cm. Find the height of cuboid?
22. Four equal cubes have side 5 cm each. They are joined together edge to edge. What will be the surface area of cuboid thus formed?
  23. The area of a rhombus is 56 cm2 and its diagonal is 7 cm. Find the length of other diagonal of the rhombus?
24. Find the maximum length of the rod that can be kept in cyboidal box of sides 30cm, 24cm and 18cm.
 25. The curved surface area of a cylinder is 216 π . If its height is 18 cm then what will be its radius?
26. 60 circular plates of equal radius are placed on each other to form a cylinder. Find height of cylinder if thickness of each plate if 3/4 cm.
27. Curved surface area of a cone is thrice and curved surface area of the other. Slant height of
second cone is thrice the slant height of first. Find ratio of their radii.
 28. A well of 2m diameter is dug 14m deep on the ground. Find the volume of earth taken out.
 29. Volume of a solid sphere is 36πcm³ . Find its radius.
30. A boy recasted a cone of 4cm height and 27cm radius into a solid sphere. Find the radiusof the sphere.
Surface Area And Volume (Chapter-11)  Answers
  1. 343m³          2. 640m³          3. 396m²          4. 3a    5. 376m²          6. 11cm           7. 1000cm³                      8. 1728cm³          9. 1000m²        10. 8cm           11. 520cm²      12. 770cm²1                3. 2714. 3 units                15. 7cm            16. 112cm or 4 7cm                17. 9cm           18. 6cm1         9. 28cm           20. 8
21. 12cm           22. 450cm²                              23. 16cm               24. √1800cm or 30 √2cm
25. 6cm            26. 45cm                                    27. 9:1            28. 44m³           29. 3cm            30. 9cm