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
A Hydrogenator water gun has a cylindrical water tank, which is 30 centimeters long. Using a hose, Jack...
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Solution:BTGmoderatorLU wrote: ↑Mon Oct 26, 2020 10:09 amSource: 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
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
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