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Question Number 18133 by Tinkutara last updated on 15/Jul/17

A 4 \times 4 \times 4 wooden cube is painted so

that one pair of opposite faces is blue,

one pair green and one pair red . The

cube is now sliced into 64 cubes of side

1 unit each .

(i) How many of the smaller cubes have

no painted face ?

(ii) How many of the smaller cubes have

exactly one painted face ?

(iii) How many of the smaller cubes have

exactly two painted face ?

(iv) How many of the smaller cubes have

exactly three painted face ?

(v) How many of the smaller cubes have

exactly one face painted blue and one

face painted green ?

Answered by sandy_suhendra last updated on 16/Jul/17

1) {(4 - 2)}^{3} = 8 (this is like volume)

2) 6 (4 - 2) = 12 (this is like surface area)

3) 12 (4 - 2) = 24 (this is like the sum of edges)

4) 8 (vertices)

5) 4 (4 - 2) = 8

Commented by Tinkutara last updated on 16/Jul/17

Thanks Sir!