• cumec of water flowing continuously for $B$ days yields a total volume of:
  $$V = 1\text{ m}^3/\text{s} \times (B \times 24 \times 3,600\text{ s}) = 86,400 B\text{ m}^3$$
• Since this water covers an area of $D$ hectares ($D \times 10,000\text{ m}^2$), the depth of water applied ($\Delta$) in meters is:
  $$\Delta\text{ (m)} = \frac{86,400 B}{10,000 D} = \frac{8.64 B}{D}\text{ meters}$$
• Converting meters into centimeters ($1\text{ m} = 100\text{ cm}$):
  $$\Delta\text{ (cm)} = \frac{8.64 B}{D} \times 100 = \frac{864 B}{D}\text{ cm}$$
• Therefore, the correct mathematical formula is $\mathbf{\Delta = \frac{864 B}{D}\text{ (cm)}}$ (Option 1).

Field water balance dynamics:

• Assertion (A) is true: The field water balance equation ($\Delta S = [P + I + U] - [ET + R + D]$) tracks all water inflows (precipitation, irrigation, capillary rise) and outflows (evapotranspiration, runoff, deep percolation), along with changes in the root-zone soil water storage ($\Delta S$).
• Reason (R) is false: The primary driving and governing forcing variables of the hydrologic budget are external hydroclimatic inputs (precipitation, irrigation) and evaporative atmospheric demand (potential evapotranspiration), while stored soil moisture is a state variable/consequence rather than the main independent driver.