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  • Question

  • The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in cm2) of curved surface areas of all small spheres?


  • Options
  • A. 31276
  • B. 36194
  • C. 25182
  • D. 33264

  • Correct Answer
  • 33264 

    • Tags: Bank Exams

    Volume and Surface Area problems

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    • 1. The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?

    • Options
    • A. 5 : 8
    • B. 4 : 9
    • C. 3 : 7
    • D. 7 : 10
      • Discuss
    • 2. A right circular cylinder has height as 18 cm and radius as 7 cm. The cylinder is cut in three equal parts (by 2 cuts parallel to base). What is the percentage increase in total surface area?

    • Options
    • A. 62
    • B. 56
    • C. 48
    • D. 52
      • Discuss
    • 3. A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216?3 cm2, then what is the height (in cm) of prism?

    • Options
    • A. 3?3
    • B. 6?3
    • C. 6
    • D. 3
      • Discuss
    • 4. PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

    • Options
    • A. 8 ? 4?2
    • B. 16 + 8?2
    • C. 16?2 ? ?16
    • D. 16 ? 8?2
      • Discuss
    • 5. A cuboid has dimensions 8 cm x 10 cm x 12 cm. It is cut into small cubes of side 2 cm. What is the percentage increase in the total surface area?

    • Options
    • A. 286.2
    • B. 314.32
    • C. 250.64
    • D. 386.5
      • Discuss
    • 6. A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm2) of each part?

    • Options
    • A. 96 + 64?2
    • B. 80 + 64?2
    • C. 96 + 48?2
    • D. 80 + 48?2
      • Discuss
    • 7. A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

    • Options
    • A. 493
    • B. 7
    • C. 14
    • D. 983
      • Discuss
    • 8. Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?

    • Options
    • A. 6.8
    • B. 13.6
    • C. 7.2
    • D. 14.4
      • Discuss
    • 9. Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

    • Options
    • A. 3.5
    • B. 3.75
    • C. 4.25
    • D. 4.45
      • Discuss
    • 10. There are 8 equidistant points A, B, C, D, E, F, G and H (in same order) on a circle. What is the value of ?FDH (in degrees)?

    • Options
    • A. 22.5
    • B. 45
    • C. 30
    • D. 42.5
      • Discuss

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