Question

There is a 3 × 3 × 3 cube which consists of twenty seven 1 × 1 × 1 cubes (see Fig. 2.3). It is ‘tunneled’ by removing cubes from the coloured squares. Find:

(i) Fraction of number of small cubes removed to the number of small cubes left in given cube.

(ii) Fraction of the number of small cubes removed to the total number of small cubes.

(iii) What part is (ii) of (i)?

Answer 1

Number of small cubes removed = 1 + 1 + 1 + 1 + 1 +1 + 1 = 7

So, required fraction = 7/20

(ii) Required fraction = 7/27

(iii) Required part is

7/27 ÷ 7/27 =  7/27 x 20/7 = 20/27