A rectangular channel of most efficient proportion has a base width of $3$m and carries water at $2\mathrm{.}70$m$^3/$s$.$ If the same material were used for the most efficient trapezoidal section, by how much would the water$-$carrying capacity be increased?

A$.0\mathrm{.}95$ m$^3/$s

B$.0\mathrm{.}61$m$^3/$s

C$.0\mathrm{.}84$m$^3/$s

D$.0\mathrm{.}73$m$^3/$s

Please provide detailed explaination.