Question

How many cuts will be required if a cube is divided into '120' identical pieces ?​

Answer 1

Answer:

17

Step-by-step explanation:

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Answer 2

Given: A cube is divided into '120' identical pieces.

To find: The number of cuts required if a cube is divided into '120' identical pieces.

Solution:

Let l, m and n be the three kinds of faces on a cube. The l represents the faces on the top and bottom, m represents the faces on the front and back and n represents the faces on the left and right. One cut on one face results in the formation of two identical pieces. So, the number of pieces formed is always one more than the number of cuts on a single face. Hence,

$(l+1) (m+1)(n+1) = 120$

$(l+1) (m+1)(n+1) = 4 * 5 * 6$

Now, the values of l, m and n can be found as follows.

$l + 1 = 4$

$l = 3$

$m + 1 = 5$

$m = 4$

$n + 1 = 6$

$n = 5$

Thus, the number of cuts required is

$cuts = 3 + 4 + 5$

       $= 12$

Therefore, the number of cuts required if a cube is divided into '120' identical pieces is 12.