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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

Answer:

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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