Since a cylinder is closely related to a prism , the formulas for their surface areas are related.
Remember the formulas for the lateral surface area of a prism is p h and the total surface area is p h + 2 B . Since the base of a cylinder is a circle, we substitute 2 π r for p and π r 2 for B where r is the radius of the base of the cylinder. So, the formula for the lateral surface area of a cylinder is L . S . A . = 2 π r h .
Example 1: Find the lateral surface area of a cylinder with a base radius of 3 inches and a height of 9 inches.
L . S . A . = 2 π ( 3 ) ( 9 ) = 54 π inches 2 ≈ 169.64 inches 2 The general formula for the total surface area of a cylinder is T . S . A . = 2 π r h + 2 π r 2 .
Example 2: Find the total surface area of a cylinder with a base radius of 5 inches and a height of 7 inches.
T . S . A . = 2 π ( 5 ) ( 7 ) + 2 π ( 5 ) 2 = 120 π inches 2 ≈ 376.99 inches 2
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$\color{green}{a.)2:9}\\ b.)4:9\\ c.)\text{cannot be determined }\\ d.) \text{none of these}\\$ I found that $h_1=h_2=h_3\\$ and $ \dfrac{A_{\text{2nd segment}}}{A_{\text{full cone}}}=\dfrac{\pi\times (1+2)\times \sqrt{h_1^2+1} }{\pi\times 3\times \sqrt{(3h_1)^2+3^2} }=\dfrac13$ But book is giving option $a.)$ $\endgroup$Last Updated: 3 June 2022 Read the Multiple Choice Questions on Volume And Surface Area of Solids to Boost and Improve your Maths Skills. These Multiple Choice Questions will help ICSE and CBSE students to prepare well for their Examinations. This chapter on Volume And Surface Area of Solids is also useful for Aspirants sitting for various Competitive Exams. Solve these Questions and Improve your Skills, Logical Reasoning, and Problem Solving ability. Volume And Surface Area Of Solids1. What is the Volume of the Cube if the Perimeter of one face of a Cube is 40 cm? 2. If the Length, Breadth, and Height of a Cuboid are 2 m, 2 m, and 1 m. What is the Surface Area in m2?a) 12b) 24c) 16 d) 8 3. A Rectangular SandBox is 5 m wide and 2 m long. How many Cubic Metres of Sand is needed to fill the Box unto a Depth of 10 cm?a) 2.5b) 1c) 5 d) 3 4. What is the Surface Area of a Cube of Side 27 Cm? 5. If the Length, Breadth, and Height of a Cuboid are in the Ratio 6 : 5 : 4 and the Total Surface Area of the Cuboid is 33300 cm2. What is the Breadth of the Cuboid?a) 95 cmb) 25 cmc) 55 cm d) 75 cm 6. The number of Bricks each measuring 25 cm x 12.5 cm x 7.5 cm required to construct a wall 6 m Long, 5 m High, and 0.5 m Thick, While the Mortar occupies 5% of the Volume of the Wall is? d) 2019 7. What is the weight of the beam if the beam is 9 m long, 40 cm wide, and 20 cm Deep is made up of iron that weighs 50 kg per cubic meter?a) 15 kgb) 39 kgc) 29 kg d) 36 kg 8. What is the length of the Longest Rod that can be placed in a room 30 m long, 24 m broad, and 18 m high?a) 45√2 mb) 15√2 mc) 30√2 m d) 60 m 9. Each brick measures 25 cm x 12.5 cm x 7.5 cm, How many Bricks will be needed to construct a wall 15 m long, 1.8 m high, and 37.5 cm thick?a) 4404b) 4320c) 6020 d) 6460 10. A Wooden Box of Dimensions 8 m x 7 m x 6 m is to carry Rectangular Boxes of dimensions 8 cm x 7 cm x 6 cm. What is the Maximum Number of Boxes that can be carried in the Wooden box?a) 99,00,000b) 10,00,000c) 12,00,000 d) 98,00,000 Related: Area And Perimeter Multiple Choice Questions (CBSE & ICSE) 11. What is the Total Surface Area of all the Small Cubes if 4 cm Cube is cut into 1 cm Cubes? 12. If each side of a Cube is doubled. What is its Volume?a) Becomes 8 timesb) Becomes doublec) Becomes 6 times d) Does not change 13. A Cube of side 6 cm is cut into a number of cubes each of side 2 cm. What is the number of Cubes so formed?a) 22b) 61c) 27 d) 24 14. If Three Cubes of Metal of edges 6 cm, 8 cm, and 10 cm are melted and made into a single cube. What is the edge of the new cube so formed?a) 92 cmb) 24 cmc) 18 cm d) 12 cm 15. If two cubes each with an 8 cm edge are joined end to end, what is the Surface Area of the resulting Cuboid? 16. The Volume of a wall, 5 times as high as it is broad and 8 times as long as it is high is 12.8 m3. What is the breadth of the wall? d) 10 cm 17. The length of the longest pole that can be placed on the floor of a room is 10m and the length of the longest pole that can be placed in a room is 10√2 m. What is the height of the room?a) 10.5 mb) 10.2 mc) 10 m d) 20 m 18. If the length of the diagonal of a cube is 4√3 cm. What is the length of its edge?a) 4 cmb) 8 cmc) 6 cm d) 2 cm 19. What is the Surface Area of a Cube if its Volume is 2744 Cm3? 20. What is the Volume of a Cube with Surface Area 384 cm2? Related: Simple Interest And Compound Interest Multiple Choice Questions 21. What is the number of Coins required, if one coin is 1.5 cm in diameter and 0.2 cm thick to be melted to form a Right Circular Cylinder of height 10 cm and diameter 4.5 cm? d) 474 22. What is the Total Surface Area of the Cylinder if the ratio between the radius of the base and the height of a Cylinder is 2 : 3 and its volume is 1617 cm3? 23. What is the ratio of the Total Surface Area to the Lateral Surface Area of a cylinder with a base radius of 80 cm and height of 20 cm?a) 2 : 3b) 4 : 1c) 5 : 1 d) 3 : 1 24. If the height of a Cylinder is 14 cm and its Curved Surface Area is 264 cm2. What is the Volume of the Cylinder? 25. What is the height of a Cylinder if the Curved Surface Area is 1760 m2and its base radius is 14 cm?a) 15 cmb) 5 cmc) 10 cm d) 20 cm 26. What is the Total Surface Area of the cylinder having a diameter of 28 cm and a height of 20 cm? 27. What is the Volume of the Cylinder whose height is 14 cm and the diameter of the base is 4 cm? 28. What is the ratio of the Surface Area if Two Cubes have their volumes in the ratio 1 : 27?a) 1 : 8b) 1 : 9c) 1 : 19 d) 1 : 21 29. 1 m3 = ________ cm3a) 10,00,000b) 10,000,000c) 10,00,000,000 d) 1,00,000 30. 1 cm3 = ________ dm3a) 0.1b) 0.01c) 0.001 d) 0.0001 Related: Time And Distance Multiple Choice Questions (Boost Your IQ) 31. If the Surface Area of a cube is numerically equal to its volume, then the edge of the cube is? d) 4 Units 32. To calculate the Area of the road paved by a road roller, we need to find the ______ of the roller?a) Areab) Curved Surface Areac) Total Surface Area d) Volume Answer b) Curved Surface Area 33. A ________, when rolled along its length or breadth, forms a Cylinder.a) Rectangleb) Squarec) Cone d) Hexagon 34. If the Volume of a Cylinder is numerically equal to its Curved Surface Area. What is the radius of the base?a) 1 Unitb) 2 Unitsc) 3 Units d) 4 Units 35. What is the Total Surface Area of a Cuboid?a) (lxbxh) Sq. Unitsb) 2[(l+b)xh] Sq. Unitsc) √(l²+b²+h²) Sq. Units d) 2(lb+bh+lh) Sq. Units Answer d) 2(lb+bh+lh) Sq. Units 36. What is the Diagonal of a Cuboid? d) √(l²+b²+h²) Sq. Units Answer c) √(l²+b²+h²) Units 37. What is the Total Surface Area of a Cube?a) 4a² Sq. Unitsb) 6a² Sq. Unitsc) 5a² Sq. Units d) a² Sq. Units 38. What is the Curved Surface Area of a Cylinder?a) πrh Sq. Unitsb) 2πrh Sq. Unitsc) 4πrh Sq. Units d) 2πr²h Sq. Units 39. What is the Volume of a Cylinder?a) πr²h Sq. Unitsb) 2πr²h Sq. Unitsc) πr²h Cubic Units d) 2πr²h Cubic Units Answer c) πr²h Cubic Units 40. What is the Total Surface Area of a Cylinder?a) 2πr²(r+h) Cubic Unitsb) 4πr²(r+h) Sq. Unitsc) 2πr(r+h) Cubic Units d) 2πr(r+h) Sq. Units Answer d) 2πr(r+h) Sq. Units Related: Exponents And Powers Multiple Choice Questions (CBSE & ICSE) 41. What is the Volume of a Cuboid? c) a3 Cubic Units d) a√3 Cubic Units Answer b) (lxbxh) Cubic Units 42. What is the Lateral Surface Area of a Cuboid?a) 2[(l+b)xh] Sq. Unitsb) 2[lx(b+h)] Sq. Unitsc) 2πr²h Sq. Units d) 2πrh Sq. Units Answer a) 2[(l+b)xh] Sq. Units 43. What is the Volume of a Cube? 44. What is the Lateral Surface Area of a Cube?a) 4a² Unitsb) 4a² Sq. Units c) 4a3 Cubic Units d) 2πrh Sq. Units 45. What is the Volume of a cuboid of length: 24 cm, breadth: 16 cm, and height: 7.5 cm? 46. What is the Diagonal of a Cube? d) a√3 Cubic Units 47. What is the Volume of a Cylinder if height: 42 cm, base radius: 10 cm? 48. What is the Total Surface Area of a Cylinder of height: 32 cm and radius: 10.5 cm? 49. A roller of diameter 84 cm and length of 120 cm takes 500 complete revolutions to level a playground, what will be the cost of leveling it at ₹4.50 per m2?a) ₹2229b) ₹9089c) ₹ 21695 d) ₹7128 50. What is the height of a cylinder if the Total Surface Area is 660 cm2 and radius 5 cm?a) 24 cmb) 20 cmc) 16 cm d) 12 cm Related: Maths General Knowledge Questions And Answers With PDF 51. If the Curved Surface Area and Volume of a Cylindrical Pillar are 264 m2 and 924 m3. What is the Diameter of the pillar?a) 21 mb) 14 mc) 7 m d) 28 m 52. How many bricks will be required to construct a wall 10 m long, 6 m high, and 22.5 cm thick, if each brick measures 25 cm x 12 cm x 9 cm?a) 5054b) 5000c) 6000 d) 9090 53. What is the length of the longest rod that can be placed in a room 16 m long, 12 m broad, and 32/3 m high?a) 66/3 mb) 67/3 mc) 68/3 m d) 69/3 m 54. The length, breadth, and height of a Cuboid are in the ratio 6:5:3. If its Total Surface Area is 504 cm2. What is the Volume of the Cube? 55. The Total Surface Area of a Cube is 384 cm2. What is the Volume? 56. What is the Volume of a Cube whose edges measure 15 cm? 57. The Volume of Cuboid is 972 m3. If its length and breadth are 16 cm and 13.5 cm. What is the height?a) 8.8 mb) 6.7 mc) 4.5 m d) 2.5 m 58. What is the length of the wire if 2200 cm3 of brass is to be drawn into a cylindrical wire of diameter 0.5 cm?a) 152 mb) 312 mc) 112 m d) 212 m 59. What is the height of a Cylinder if the Total Surface Area is 660 cm2 and the radius is 5 cm?a) 16 cmb) 26 cmc) 84 cm d) 660 cm 60. A swimming pool 70 m x 44 m x 3 m is filled by water from a pipe of diameter 35 cm at 6 m per second. What is the time required to fill the pool?a) 30/9 hoursb) 10/9 hoursc) 20/9 hours d) 40/9 hours Related: AFCAT Exams: Why Practice Is Important? (2022) 61. How many Cubic Metres of the earth must be dug out to sink a well 22.5 m deep that has a diameter of 7m? 62. A well is dug 8 m deep, it has a diameter of 14 m. What is the height of the embankment if the earth taken out of it has been evenly spread all around to form an embankment of width 21 m?a) 49.8 mb) 14 mc) 8 m d) 53.3 m 63. The Total Surface Area of a Solid Cylinder is 462 cm2 and its Curved Surface Area is one-third of its Total Surface Area. What is the Volume of the Cylinder? 64. A 20 m deep well with a diameter of 7 m is dug up and the earth from digging is spread evenly to form a platform 22m x 14 m. Find the height of the platform?a) 2.5 mb) 3.5 mc) 4.5 m d) 5.5 m 65. A classroom is 10 m long, 6.4 m broad, and 5m high. If each student is given 1.6 m2 of the floor area. How many students can be accommodated in the room?a) 50b) 30c) 20 d) 40 66. The length, breadth, and height of a room are 8m, 6.5 m, and 3.5 m. What is the area of 4 walls of the room? 67. Find the Lateral Surface Area of the new Cube formed if the three cubes of metal with edges 5 cm, 4 cm, 3 cm are melted to form a single cube? 68. What is the length of each edge of the cube if a solid piece of metal in the form of a cuboid of dimensions 24 cm x 18 cm x 4 cm is melted down and recast into a cube?a) 16 cmb) 8 cmc) 10 cm d) 12 cm 69. If the Areas of the three adjacent faces of a cuboidal box are 120 cm2, 72 cm2, 60 cm2. What is the Volume of the Box? 70. How many planks can be stored in a place 15 m long, 4 m wide, and 60 m deep if each measures 5 m x 24 cm x 10 cm?a) 200b) 150c) 300 d) 100 Advertisement |