Mensuration Questions Answers

Mensuration - Quant/Math - CAT 2008

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)

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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