Question:
A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 6
Solution:
The correct answer is option (c) 1: 4
Explanation:
Given: The cube side is 4cm
The side of cube 4cm is cut into small cubes, in which each of 1 cm
Therefore, the total number of cubes = 4 x 16 = 64 cubes
Thus, the number of cut-out cubes = 64/1
Now, the surface area of the cut-out cubes = c x 1 cm2
The surface area of the original cube = 6 x 42
Hence, the required ratio obtained is:
= 6 x 42 / = 64 x 6
= 1: 4
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