A farmer is using a soil moisture sensor to guide his irrigation decisions. The sensor measures an average volumetric water content of $0\mathrm{.}19c{m}^{3}c{m}^{-3}$ in the $18-$inch deep root$-$zone of the crop. How many inches of irrigation water should the farmer apply to increase the water content to $0\mathrm{.}30c{m}^{3}c{m}^{-3}$ in each of the following scenarios?

See the video that demonstrates how to apply the soil water balance equation to solve problems like this linked on p$.108.$

a$.$ Using a furrow irrigation system in which $15\%$ of the applied water is lost to runoff and $10\%$ is lost to evaporation.

b$.$ Using a center pivot irrigation system in which $5\%$ of the applied water is lost to runoff and $10\%$ is lost to evaporation.

c$.$ Using a drip irrigation system where none of the water is lost to runoff and $5\%$ is lost to evaporation.