VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

21. A semi-circular plate is rolled up to form a conical surface. The angle between the generator and the axis of the cone is [2018 (II) Evening Shift]

Correct Answer: (c) 30º
Solution:Clearly, the radius of semi-circle = slant height of cone = r

22. A solid right cylinder is of height π cm. If its lateral surface area is half its total surface area, then the radius of its base is [2018 (II) Evening Shift]

Correct Answer: (b) π cm
Solution:Height of cylinder = π cm

23. A rectangular block of length 20 cm, breadth 15 cm and height 10 cm is cut up into exact number of equal cubes. The least possible number of cubes will be [2018 (II) Evening Shift]

Correct Answer: (d) 24
Solution:

24. If the diagonal of a cube is of length l, then the total surface area of the cube is [2018 (II) Evening Shift]

Correct Answer: (d) 2l²
Solution:

25. Two cones have their heights in the ratio 1 : 3. If the radii of their bases are in the ratio 3 : 1, then the ratio of their volumes will be [2018 (II) Evening Shift]

Correct Answer: (c) 3 : 1
Solution:Let the height of cones be h and 3h and their radii of bases be 3r and r.

26. The radius and slant height of a right circular cone are 5 cm and 13 cm respectively. What is the volume of the cone? [2018 (I) Morning Shift]

Correct Answer: (a) 100 π cm³
Solution:Radius of cone = 5 cm = r


27. A right circular cone is sliced into a smaller cone and a frustum of a cone by a plane perpendicular to its axis. The volume of the smaller cone and the frustum of the cone are in the ratio 64 : 61. Then, their curved surface areas are in the ratio [2018 (I) Morning Shift]

Correct Answer: (b) 16 : 9
Solution:According to the question,


28. There are as many square centimetres in the surface area of a sphere as there are cubic centimetres in its volume. What is the radius of the sphere? [2018 (I) Morning Shift]

Correct Answer: (b) 3 cm
Solution:Given, surface area of sphere = Volume of sphere

29. The curved surface area of a right circular cone is 1.76 m 2 and its base diameter is 140 cm. What is the height of the cone? [2018 (I) Morning Shift]

Correct Answer: (d) 10√15 cm
Solution:Diameter = 140 cm


30. A cube of maximum volume (each corner touching the surface from inside) is cut from a sphere. What is the ratio of the volume of the cube to that of the sphere? [2018 (I) Morning Shift]

Correct Answer: (c) 2 : √3 π
Solution:Let the edge of the cube be a cm