$12\mathrm{.}70$ Estimate the total time required to empty a tank which is a paraboloid of revolution with every horizontal section a circle whose radius equals the square root of the height above the bottom, through which is cut a $25-$mm$-$round sharp$-$edged orifice. The depth of water at the start of time is $3\mathrm{.}0$ meters. Refer to Exhibit $12\mathrm{.}70.$

a$.2$ hr $20$ min

b$.2$ hr $5$ min

c$.1$ hr $50$ min

d$.1$ hr $38$ min