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Mensuration - Quant/Math - CAT 2013

  1. Algebra
  2. Progressions
  3. Averages
  4. Clocks and Calendars
  5. Data Sufficiency
  6. English Grammar
  7. Function
  8. Geometry
  9. Coordinate Geometry
  10. Interest
  11. Mensuration
  12. Mixtures & Alligations
  13. Number System
  14. Percentages
  15. Permutation & Combination
  16. Pipes & Cisterns And Work & Time
  17. Probability
  18. Profit & Loss
  19. Races
  20. Ratio, Proportion
  21. Speed, Time & Distance
  22. Trigonometry
  23. Miscellaneous
  24. General Knowledge
Question 4 the day: July 31, 2003

The question for the day is from the topic of Mensuration.
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

(1) 1 : 6 (2) 1 : 5
(3) 1 : 25 (4) 1 : 125
Correct Answer - (2)

Solution:


The volume of the larger cube = 53 = 125 cm3.

The volume of each of the smaller cubes = 13 = 1 cm3. Therefore, one would get 125 smaller cubes.

The surface area of the larger cube = 6a2 = 6(52) = 6 * 25 = 150

The surface area of each of the smaller cubes = 6 (12) = 6.

Therefore, surface area of all of the 125, 1 cm3 cubes = 125 * 6 = 750.

Therefore, the required ratio = 150 : 750 = 1 : 5




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