
Mensuration  Quant/Math  CAT 2013
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 = 5^{3} = 125 cm^{3}.
The volume of each of the smaller cubes = 1^{3} = 1 cm^{3}. Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a^{2} = 6(5^{2}) = 6 * 25 = 150
The surface area of each of the smaller cubes = 6 (1^{2}) = 6.
Therefore, surface area of all of the 125, 1 cm^{3} cubes = 125 * 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5



