VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

51. The radius of the base and the height of a solid right circular cylinder are in the ratio 2 : 3 and its volume is 1617 cm 3 . What is the total surface area of the cylinder? [2016 (II) Evening Shift]

Correct Answer: (c) 770 cm²
Solution:Let radius of the base be 2x. Height of the cylinder be 3x and volume = 1617 cm³.


52. The cost of painting a spherical vessel of diameter 14 cm is ₹8008. What is the cost of painting per square centimetre? [2016 (II) Evening Shift]

Correct Answer: (c) ₹13
Solution:Given, diameter of vessel is 14 cm and cost of painting is ₹8008.

53. A drinking glass of height 24 cm is in the shape of frustum of a cone and diameters of its bottom and top circular ends are 4 cm and 18 cm respectively. If we take capacity of the glass as πx cm³, then what is the value of x? [2016 (II) Evening Shift]

Correct Answer: (a) 824
Solution:Here, h = 24 cm, r = 4/2 cm = 2 cm

54. Rain water from a roof of 22m × 20m drains into a cylindrical vessel having diameter of base 2m and height 3.5 m. If the vessel is just full, what is the rainfall? [2016 (II) Evening Shift]

Correct Answer: (c) 2.5 cm
Solution:Given, area of roof = length × breadth = 22m × 20m

55. The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is 1/64 the volume of original cone. What is the height from the base at which the section is made? [2016 (II) Evening Shift]

Correct Answer: (d) 45 cm
Solution:In ∆AOE and ∆ADC, ∵ ∆AOE ∼ ∆ADC

56. The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm², what is the volume of the cylinder? [2016 (II) Evening Shift]

Correct Answer: (c) 1078 cm³
Solution:Let r and h be the radius and height of cylinder.

57. A cubic metre of copper weighing 9000 kg is rolled into a square bar 9 m long. An exact cube is cut off from the bar. How much does the cube weigh? [2016 (II) Evening Shift]

Correct Answer: (b) 1000/3 kg
Solution:Density of copper = Mass/Volume

58. Into a conical tent of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be emptied, if space required for the wheat in each bag is 1.96 m³ ? [2016 (II) Evening Shift]

Correct Answer: (c) 132
Solution:

59. A pipe with square cross-section is supplying water to a cistern which was initially empty. The area of cross-section is 4 cm2 and the nozzle velocity of water is 40m/s. The dimensions of the cistern 10m × 8m × 6m. Then, the cistern will be full in [2015 (II) Evening Shift]

Correct Answer: (c) 8 h and 20 min
Solution:We have, area of cross-section of pipe

60. A hollow cylindrical drum has internal diameter of 30 cm and a height of 1 m. What is the maximum number of cylindrical boxes of diameter 10 cm and height 10 cm each that can be packed in the drum? [2015 (II) Evening Shift]

Correct Answer: (d) 90
Solution:Let n cylindrical boxes be packed n ⋅ π × 5 × 5 × 10 = π × 15 × 15 × 100
∴ n = 90 boxes