BTGmoderatorDC wrote:A Hydrogenator water gun has a cylindrical water tank, which is 30 centimeters long. Using a hose, Jack fills his Hydrogenator with π cubic centimeters of his water tank every second. If it takes him 8 minutes to fill the tank with water, what is the diameter of the circular base of the gun's water tank?

A. 1 cm
B. 2 cm
C. 4 cm
D. 8 cm
E. 16 cm
Source: Manhattan Prep

$$H = 30\,{\rm{cm}}\,\,\,\,\,\,\,{\rm{;}}\,\,\,\,\,\,\,{{\pi \,\,{\rm{c}}{{\rm{m}}^3}} \over {\,1\,\,{\rm{second}}\,}}\,\,\,{\rm{filling}}\,\,{\rm{rate}}$$
$${\rm{?}}\,\,{\rm{ = }}\,\,D\,\,\,\left[ {{\rm{cm}}} \right]$$

Let´s use UNITS CONTROL, one of the most powerful tools of our method:

$${\rm{8}}\,{\rm{minutes}}\,\, \cdot \left( {{{\,60\,\,{\rm{seconds}}\,} \over {1\,\,{\rm{minute}}}}} \right)\,\,\,\left( {{{\pi \,\,{\rm{c}}{{\rm{m}}^3}} \over {\,1\,\,{\rm{second}}\,}}} \right)\,\,\, = \,\,\,\pi {\left( {{D \over 2}} \right)^2}H\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\,\, = {V_{{\rm{cylinder}}}}\,\,\left[ {{\rm{c}}{{\rm{m}}^3}} \right]\,\,\,} \right]$$
$$8 \cdot 60 = {\left( {{D \over 2}} \right)^2} \cdot 30\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\left( {{D \over 2}} \right)^2} = 16\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{D\, > \,0} \,\,\,\,\,\,\,\,{D \over 2} = 4\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = D = 8\,\,\,\,\,\,\,\,$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.