A hemispherical tank of radius (R) has an orifice of cross-sectional area (a) at its bottom and is full of liquid. The time required to empty the tank completely is

A. $$\frac{{14\pi {{\text{R}}^{\frac{1}{2}}}}}{{15{{\text{C}}_{\text{d}}} \times {\text{a}}\sqrt {2{\text{g}}} }}$$

B. $$\frac{{14\pi {{\text{R}}^{\frac{3}{2}}}}}{{15{{\text{C}}_{\text{d}}} \times {\text{a}}\sqrt {2{\text{g}}} }}$$

C. $$\frac{{14\pi {{\text{R}}^{\frac{5}{2}}}}}{{15{{\text{C}}_{\text{d}}} \times {\text{a}}\sqrt {2{\text{g}}} }}$$

D. $$\frac{{14\pi {{\text{R}}^{\frac{7}{2}}}}}{{15{{\text{C}}_{\text{d}}} \times {\text{a}}\sqrt {2{\text{g}}} }}$$

Answer: Option C