A Hydrogenator water gun has a cylindrical water tank, which is 30

Question

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

Kudos for a correct solution.

A. 1 cm
B. 2 cm
C. 4 cm
D. 8 cm
E. 16 cm

Kudos for a correct  solution .

NickHalden · Answer

Formula used : Volume of a cylinder = area of base * height = π*r*r*h

Filling rate = π cm cube per sec ----------- (1)
Total time to fill = 8 mins = 480 secs ------------ (2)

From 1 & 2, Total volume filled = π*480 -------------- (3)

Now, we know that 
π*r*r*30 = Total volume ----------- (4)

Solving 3 & 4,
r = 4
 Hence C !!

xLUCAJx · Answer

I did all that you did but since it asks for the diameter shouldn't it be 8 (4*2)?

peachfuzz · Answer

Volume as filled by hose=60×8×pi

Volume of cylinder=pi×r^2×30

60×8×pi=pi×r^2×30
r=4 so diameter=8

Answer:

D. 8 cm

adityadon · Answer

volume = 480 *pi

Pi*r^2*h = 480 pi 
r^2 * 30 = 480

so r = 4
And diameter = 8

kanigmat011 · Answer

D is correct
Volume as filled by hose=60×8×pi

Volume of cylinder=pi×r^2×30

60×8×pi=pi×r^2×30
r=4 so diameter = 8

ENGRTOMBA2018 · Answer

Height of the cylinder = h = 30 cm

Rate of filling the tank = R =  \pi \frac{{cm}^3}{s}

Time it takes to fill the tank = t=8 minutes = 480 seconds

Thus, volume of the cylinder (with radius of the base of the base of the cylinder = r cm) = V = R*t =  480\pi  =  \pi*r^2*h

Thus r = 4 cm and diameter = 2r =8 cm. D is the correct answer.

KS15 · Answer

Height of cylinder tank=30 cm
Rate of filling = Pie cu cm per second
8 minutes=8*60=480 seconds
Volume of tank =pie r^2*h=pie*r^2*30=480 pie
radius=4 cm
diamter=8 cm
Answer D

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

In 8 minutes, or 480 seconds,  480\pi  cm3 of water flows into the tank. Therefore, the volume of the tank is  480\pi . You are given a height of 30, so you can solve for the radius:

V = \pi r^2 * h

480\pi = 30\pi r^2

r^2 = 16

r= 4

Therefore, the diameter of the tanks base is 8 cm.

Answer: D.

stonecold · Answer

A hydrogenator water gun has a cylinderical water tank ; which is 30 cm long .Using a hose, jack fills the tank with π cubic cm of water every scond. If it takes 8 minutes to fill the tank completely with water => the diameter of the tank is 
  4
  8
  12
  16
  20

Bunuel · Answer

Merging topics. Please refer to the discussion above.

fskilnik · Answer

H = 30\,{\rm{cm}}\,\,\,\,\,\,\,{\rm{;}}\,\,\,\,\,\,\,{{\pi \,\,{\rm{c}}{{\rm{m}}^3}} \over {\,1\,\,{\rm{second}}\,}}\,\,\,{\rm{filling}}\,\,{\rm{rate}}

{\rm{?}}\,\,{\rm{ = }}\,\,D\,\,\,\left

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 \,\,\,} \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.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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A Hydrogenator water gun has a cylindrical water tank, which is 30

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A Hydrogenator water gun has a cylindrical water tank, which is 30

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