VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

71. A river 2 5. m deep and 45m wide is flowing at the speed of 3.6 km/h. The amount of water that runs into the sea per minute, is [2015 (II) Evening Shift]

Correct Answer: (b) 6750 m
Solution:We have, speed of water = 3.6 km/h

72. A sphere and a cube have same surface area. The ratio of square of their volumes is [2015 (I) Morning Shift]

Correct Answer: (a) 6 : π
Solution:Let the radius of the sphere and side of cube be r and a respectively.


73. The radius of a sphere is equal to the radius of the base of a right circular cone and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is [2015 (I) Morning Shift]

Correct Answer: (a) 2 : 1
Solution:Let radius of sphere and cone be r.

74. Water flows through a cylindrical pipe of internal diameter 7 cm at the rate of 5 m/s. The time, in minutes, the pipe would take to fill an empty rectangular tank 4m × 3m × 2.31m is [2015 (I) Morning Shift]

Correct Answer: (b) 24
Solution:Given, diameter of cylindrical pipe = 7 cm

75. The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is [2015 (I) Morning Shift]

Correct Answer: (d) 273 π square cm
Solution:Let the slant height of cone be l cm. Given, h = 24 cm and r = 7 cm

76. A rectangular block of wood having dimensions 3m × 2m × 1.75m has to be painted on all its faces. The layer of paint must be 0.1 mm thick. Paint comes in cubical boxes having their edges equal to 10 cm. The minimum number of boxes of paint to be purchased is [2015 (I) Morning Shift]

Correct Answer: (c) 3
Solution:Given, dimensions of a rectangular block of wood is 3m, 2m and 1.75 m.

77. Simplify the question [2015 (I) Morning Shift]

Correct Answer: (c) 664 sq units
Solution:Let the dimensional of cuboid be l, b and h, respectively.



78. A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is [2015 (I) Morning Shift]

Correct Answer: (c) 7 cm
Solution:Given, a rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper.

79. If three metallic spheres of radii 6 cm, 8 cm and10 cm are melted to form a single sphere, then the diameter of the new sphere will be [2015 (I) Morning Shift]

Correct Answer: (b) 24 cm
Solution:Since, three metallic spheres are melted to form a single sphere.

80. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by [2015 (I) Morning Shift]

Correct Answer: (c) 2.25 cm
Solution:Let the radius of cylindrical vessel and solid sphere be R cm and r cm, respectively.