'a' is inversely proportional to the cube of 'b'. The value of 'b' is 2 when the value of 'a' is 3. Then find the value of 'b' when the value of 'a' is \(\frac{8}{9}\):

3

ATQ,

a = \(\frac{1}{b^3} K\) 

3 = \(\frac{1}{2^3} K\)

3 = \(\frac{1}{8}\) K

K= 24

Now,

\(\frac{8}{9}\) = \(\frac{1}{b^3}\) K

b³ = \(\frac{9}{8}\) × 24

b³ = 9 × 3 = 27

b = 3