studycbse.online

Class 9 Maths Part 2 Chapter 14 – Math of Space: Surface Area and Volume | Ganita Manjari Worksheet

Practise Class 9 Maths Part 2 Chapter 14 – Math of Space: Surface Area and Volume with this Ganita Manjari worksheet. Prepare more with important questions and revision exercises designed to strengthen understanding of surface area and volume, improve mathematical practice and support effective preparation for class tests and examinations.

Fresh Worksheet: Math of Space

Surface Area and Volume

Name: ____________________
Class: ____________________
Date: ____________________
Instructions: Show all important steps. Use π = 22/7 unless another value is specified. Write appropriate units with your answers.

Section A — Quick Concept Check

1. What is the difference between surface area and volume?
2. A cube has side 7 cm. Write the formula you would use to find its total surface area.
3. Complete the following:
(a) Volume of a cuboid = ____________
(b) Volume of a cylinder = ____________
(c) Volume of a cone = ____________
(d) Surface area of a sphere = ____________
(e) Volume of a hemisphere = ____________
4. State whether each statement is True or False.
  1. The volume of a cone is three times the volume of a cylinder having the same base and height.
  2. The total surface area of a cube of side a is 6a².
  3. The curved surface area of a cylinder depends on its radius and height.
  4. A sphere has a flat circular face.
  5. The volume of a hemisphere is half the volume of the corresponding sphere.
5. Match the solid with the correct formula.
Cuboid       —      4/3πr³
Cylinder      —      lwh
Cone         —      πr²h
Sphere        —      1/3πr²h

Section B — Cuboids and Cubes

6. Find the volume and total surface area of a cuboid measuring 12 cm × 8 cm × 5 cm.
7. A cube has a total surface area of 864 cm². Find its side and volume.
8. A rectangular water tank is 4 m long, 2.5 m wide and 1.8 m deep. Find its capacity in litres.
9. A cuboidal box has a volume of 2160 cm³. Its length is 15 cm and breadth is 12 cm. Find its height.
10. A cube of side 10 cm is cut into cubes of side 2 cm. How many smaller cubes are obtained?
11. The dimensions of a cuboid are doubled. By what factor does its volume increase?
12. The side of a cube is increased from 5 cm to 10 cm. Find the ratio of the original volume to the new volume.
13. A wooden cuboid of dimensions 20 cm × 15 cm × 10 cm is painted on all its faces. Find the total area that is painted.

Section C — Cylinders

14. A cylinder has radius 7 cm and height 15 cm. Find its volume.
15. Find the curved surface area of a cylinder of radius 3.5 cm and height 20 cm.
16. A cylindrical tank has diameter 2 m and height 3 m. Find its volume in cubic metres.
17. A cylinder has volume 1540 cm³ and radius 7 cm. Find its height.
18. A cylindrical pipe has an external radius of 5 cm and length 2 m. Find its curved surface area in cm².
19. The radius of a cylinder is doubled while its height remains unchanged. How many times does its volume become?
20. Two cylinders have the same volume. The radius of the first is twice the radius of the second. Find the ratio of their heights.
21. A cylindrical container has radius 10 cm and height 30 cm. How many litres of water can it hold?

Section D — Cones

22. A cone has radius 7 cm and height 24 cm. Find its slant height.
23. Find the volume of a cone with radius 6 cm and height 14 cm.
24. Find the curved surface area of a cone with radius 7 cm and slant height 25 cm.
25. A cone has height 12 cm and slant height 13 cm. Find its radius.
26. A conical tent has radius 5 m and height 12 m. Find the amount of canvas required to cover its curved surface.
27. A cone and a cylinder have the same radius and the same height. What is the ratio of their volumes?
28. The radius of a cone is 10 cm and its slant height is 26 cm. Find its height.

Section E — Spheres and Hemispheres

29. Find the surface area of a sphere of radius 7 cm.
30. Find the volume of a sphere of radius 3.5 cm.
31. Find the curved surface area of a hemisphere of radius 14 cm.
32. Find the total surface area of a hemisphere of radius 7 cm.
33. A spherical ball has radius 10.5 cm. Find its volume.
34. A sphere and a hemisphere have the same radius. Find the ratio of their volumes.
35. The radius of a sphere is tripled. By what factor does its volume increase?
36. A hemispherical bowl has radius 10.5 cm. Find its capacity in litres.

Section F — Mixed Application Questions

37. A cuboidal tank measures 3 m × 2 m × 1.5 m. Water is poured into it to a height of 1 m. Find the volume of water in litres.
38. A solid cube of side 6 cm is melted and recast into spheres of radius 1 cm. Find the number of complete spheres that can be made.
39. A cylindrical bucket has radius 14 cm and height 30 cm. How much water can it hold in litres?
40. A cone has radius 3.5 cm and height 12 cm. A cylinder has the same radius and height. Find the difference between their volumes.
41. A cube has volume 729 cm³. Find its total surface area.
42. A cylindrical vessel has radius 7 cm. If its volume is 2156 cm³, find its height.
43. A spherical tank has radius 3 m. Find its capacity in litres.
44. A cuboid has dimensions 10 cm × 8 cm × 6 cm. A cube of side 4 cm is placed inside it. What fraction of the cuboid’s volume is occupied by the cube?
45. A cylindrical rod has radius 2 cm and height 21 cm. It is melted to form a sphere. Find the radius of the sphere.

Section G — Higher Order Thinking

46. Two cubes have sides in the ratio 2:3. Find the ratio of their volumes and total surface areas.
47. Two cylinders have equal heights. Their radii are in the ratio 2:5. Find the ratio of their volumes.
48. A sphere and a cylinder have equal radii and equal volumes. If the radius is r, find the height of the cylinder in terms of r.
49. A cone and a hemisphere have equal radii and equal volumes. If the common radius is r, find the height of the cone.
50. A cuboid has dimensions l, w and h. If all three dimensions are increased by 10%, will its volume increase by 10%? Explain with a mathematical expression.
51. A sphere is cut into two equal hemispheres. Compare the total surface area of the two hemispheres with the surface area of the original sphere. Explain why they are different.
52. A cube and a sphere have the same volume. Which one has greater surface area? Investigate using a convenient numerical example.

Section H — Guesstimate and Real-Life Mathematics

53. Estimate the amount of water required to fill a household water tank. Measure or estimate its dimensions and show your calculation.
54. Estimate how many tennis balls could fit inside your classroom. Clearly state the assumptions you make.
55. Estimate the amount of paint required to paint the four walls of your classroom. Ignore doors and windows initially, and then subtract their areas.
56. Estimate how many books could be stored in a rectangular cupboard. Measure the approximate dimensions of the cupboard and one book.
57. A water bottle is approximately cylindrical. Measure its radius and height and estimate its capacity in millilitres.

Challenge Corner

58. A cube has side 12 cm. It is cut into smaller cubes of side 3 cm. Compare the total surface area of all the small cubes with the surface area of the original cube.
59. A cylinder has radius 7 cm and height 10 cm. Another cylinder has radius 5 cm and height 14 cm. Which cylinder has greater volume? Show your calculation.
60. A solid consists of a cylinder with a hemisphere attached to its top. The common radius is 7 cm and the height of the cylindrical part is 20 cm. Find the total volume of the solid.
61. A cone has the same base and height as a cylinder. If the cylinder has volume 900 cm³, find the volume of the cone.
62. A spherical ball has its radius increased from 4 cm to 8 cm. Find the factor by which its surface area and volume increase.
63. A cuboidal box has dimensions 30 cm × 20 cm × 15 cm. It is filled with cubes of side 5 cm. How many cubes can fit inside the box?
64. A cylindrical container and a cuboidal container have the same height and the same volume. If the cylindrical container has radius 7 cm and the cuboidal container has a square base, find the side of the square base.

Answer Key

Use this section after completing the worksheet.
  1. Surface area measures the outer surface; volume measures the space occupied.
  2. 6a²
  3. (a) lwh   (b) πr²h   (c) 1/3πr²h   (d) 4πr²   (e) 2/3πr³
  4. False, True, True, False, True
  5. Cuboid–lwh; Cylinder–πr²h; Cone–1/3πr²h; Sphere–4/3πr³
  6. Volume = 480 cm³; TSA = 392 cm²
  7. Side = 12 cm; Volume = 1728 cm³
  8. 18,000 litres
  9. Height = 12 cm
  10. 125 cubes
  11. 8 times
  12. 1 : 8
  13. 1300 cm²
  14. 2310 cm³
  15. 440 cm²
  16. 3π m³
  17. 10 cm
  18. 628.57 cm²
  19. 4 times
  20. 1 : 4
  21. Approximately 9.43 litres
  22. 25 cm
  23. 168π cm³
  24. 550 cm²
  25. 5 cm
  26. 408.33 m² approximately
  27. 1 : 3
  28. 24 cm
  29. 616 cm²
  30. approximately 179.67 cm³
  31. 1232 cm²
  32. 462 cm²
  33. approximately 4851.85 cm³
  34. 2 : 1
  35. 27 times
  36. approximately 2.31 litres
  37. 9 m³ of water = 9000 litres
  38. Approximately 36 complete spheres
  39. 18.48 litres
  40. Difference = 196π cm³
  41. Surface area = 486 cm²
  42. 14 cm
  43. Approximately 113.1 m³ = 113,100 litres
  44. 64/480 = 2/15
  45. Radius = approximately 5.5 cm
  46. Volumes ratio = 8 : 27; surface areas ratio = 4 : 9
  47. 4 : 25
  48. Height = 4r/3
  49. Height = 2r
  50. No. Volume becomes 1.1³ = 1.331 times.
  51. The two hemispheres have additional circular bases, so their total surface area is greater.
  52. Depends on the chosen common volume; calculate both surface areas using the relevant formulas.
  53. Depends on measurements and assumptions.
  54. Depends on classroom dimensions and assumptions.
  55. Depends on measurements of walls, doors and windows.
  56. Depends on cupboard and book dimensions.
  57. Use V = πr²h and 1 cm³ = 1 mL.
  58. Small-cube total surface area is greater because cutting creates additional exposed surfaces.
  59. Compare π × 7² × 10 and π × 5² × 14.
  60. Volume = cylinder volume + hemisphere volume.
  61. 300 cm³
  62. Surface area increases by 4 times; volume increases by 8 times.
  63. 72 cubes
  64. Square side = 7√π cm, approximately 12.41 cm.
Fresh Worksheet — Math of Space: Surface Area and Volume
Practice • Apply • Think • Estimate

Class 9 Maths Part 2 Chapter 14 Worksheet, Class 9 Maths Chapter 14 Worksheet, Class 9 Ganita Manjari Chapter 14 Worksheet, Class 9 Ganita Manjari Part 2 Chapter 14 Worksheet, Class 9 Maths Part 2 Chapter 14 Practice Worksheet, Class 9 Maths Chapter 14 Practice Worksheet, Class 9 Ganita Manjari Chapter 14 Practice Worksheet, Class 9 Maths Chapter 14 Worksheet Questions, Class 9 Maths Part 2 Chapter 14 Worksheet Questions, Class 9 Ganita Manjari Chapter 14 Worksheet Questions, Class 9 Maths Chapter 14 Revision Worksheet, Class 9 Ganita Manjari Chapter 14 Revision Worksheet, NCERT Class 9 Maths Chapter 14 Worksheet, NCERT Class 9 Mathematics Part 2 Chapter 14 Worksheet, CBSE Class 9 Maths Chapter 14 Worksheet, Class 9 Maths Chapter 14 Surface Area and Volume Worksheet