A Hydrogenator water gun has a cylindrical water tank, which is 30 centimeters long. Using a hose, Jack...

BTGmoderatorLU wrote: ↑

Mon Oct 26, 2020 10:09 am

Source: Manhattan Prep

A Hydrogenator water gun has a cylindrical water tank, which is 30 centimeters long. Using a hose, Jack fills his Hydrogenator with \(\pi\) 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

The OA is D

Solution:

We can let r = the radius of the circular base of the gun's water tank, so the volume of the tank is:

V = πr^2 x 30

V = 30πr^2

Since the tank is filled with π cubic centimeters of water every second, and it takes 8 minutes, or 480 seconds, to fill the tank, the volume of the tank is also:

V = 480π

Therefore, we have:

30πr^2 = 480π

r^2 = 16

r = 4

Therefore, the diameter of the circular base of the gun's water tank is 2 x 4 = 8 cm.

Answer: D