66) Choose the correct option from the following listed formula. (Note: n_a is the % of air void, a_c is the air content & n is the soil’s porosity.)

a) n_a = n x a_c

b) n_a= n/(a_c )

c) n_a= n + a_c

d) n_a= n – a_c

**Answer: a) n_a = n x a_c **

Explanation:The percentage of air voids is the ratio of the volume of air to the total volume. i.e. , n_a = (V_a )/V ……(i)

The air content is simply the ratio of the volume of air to the volume of the void.

i.e. , a_c = (V_a )/V_v ∴ V_a= a_c. V_v……(ii)

From the equation (i) & (ii),

We get, n_a = (a_c.V_v )/V

The ratio of the volume of the void to the total volume is nothing but the porosity. i.e. n = ( V_v )/V

∴ n_a = n x a_cTherefore, the product of porosity & air content is nothing but a percentage of air voids.