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The six faces of a cube are painted black.  The cube is then cut into $3^3$ smaller cubes, all the same size.

 

(a) How many of the smaller cubes have exactly one black face?

(b) How many of the smaller cubes do not have any black faces?

(c)  One of the small cubes is chosen at random, and rolled.  What is the probability that when it lands, the face on the top is black?

 Jan 21, 2024
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Asumming the big cube is cut into 27 smaller cube

(a) There are only 6 cubes with one black face,

(b)  there are only 1 cube that does not have any black faces

(c) The probabilty would be 54/162 or 1/3 because  there are 27 cubes and 162 faces,and only 54 faces are colored black the probabilty woulud be 54/162 or 1/3

 Jan 21, 2024

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