VOLUME AND SURFACE AREA (CDS)

Total Questions: 106

11. A right circular cone has height 8 cm. If the radius of its base is 6 cm, then what is its total surface area? [2019 (II) Evening Shift]

Correct Answer: (a) 96π cm²
Solution:Given,


12. Six cubes, each with 12 cm edge are joined end to end. What is the surface area of resulting cuboid? [2019 (II) Evening Shift]

Correct Answer: (c) 3744 cm²
Solution:When six cubes are joined end to end, then resulting solid is a cuboid.

13. The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area? [2019 (I) Morning Shift]

Correct Answer: (a) 300%
Solution:


14. What is the ratio of the volume of the sphere to that of the cone? [2019 (I) Morning Shift]

Correct Answer: (a) 6√3 : 1
Solution:



15. What is the ratio of the volume of the cube to that of the cylinder? [2019 (I) Morning Shift]

Correct Answer: (c) 14 : 11
Solution:Volume of cube : Volume of cylinder

16. Consider the following statements : [2019 (I) Morning Shift]

1. The surface area of the sphere is √5 times the curved surface area of the cone.
2. The surface area of the cube is equal to the curved surface area of the cylinder.

Which of the above statements is/are correct?

Correct Answer: (d) Neither 1 nor 2
Solution:Surface area of the sphere is √5 times of the curved surface area of cone.


17. (Questions 17 and 18) Read the given information carefully and answer the given question below. [2019 (I) Morning Shift]

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.

What is the surface area of the cuboid?

Correct Answer: (a) 288 cm²
Solution:Length of cuboid = l, Breadth of cuboid = b, Height of cuboid = h

18. If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S - 3V) equal to ? [2019 (I) Morning Shift]

Correct Answer: (c) 1144 cm³
Solution:S is the sum of the cube of the dimensions of the cuboid. S = l³ + b³ + h³, V = lbh

19. Walls (excluding roofs and floors) of 5 identical rooms having length, breadth and height 6 m, 4 m and 2.5 m respectively are to be painted. Out of five rooms, two rooms have one square window each having a side of 2.5 m. Paints are available only in cans of 1 L; and 1 L of paint can be used for painting 20 m² . The number of cans required for painting is [2018 (II) Evening Shift]

Correct Answer: (b) 12
Solution:Length (l) , breadth (b), and height (h) of walls are 6m, 4m and 2.5 m respectively

20. The lateral surface area of a cone is 462 cm² . Its slant height is 35 cm. The radius of the base of the cone is [2018 (II) Evening Shift]

Correct Answer: (c) 4.2 cm
Solution:Lateral surface area of cone = πrl, ∴ 462 = πr(35) [∵ l = 35]