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# A cylindrical water tank has a diameter of 14 meters and a height of

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Math Expert
Joined: 02 Sep 2009
Posts: 52360
A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Jul 2015, 00:35
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:12) correct 24% (01:26) wrong based on 165 sessions

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A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill $$\pi$$ cubic meters of the tank every minute. How long will it take the water truck to fill the water tank from empty to half-full?

A. 140 minutes
B. 245 minutes
C. 280 minutes
D. 490 minutes
E. 980 minutes

Kudos for a correct solution.

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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Jul 2015, 02:29
1
Bunuel wrote:
A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill $$\pi$$ cubic meters of the tank every minute. How long will it take the water truck to fill the water tank from empty to half-full?

A. 140 minutes
B. 245 minutes
C. 280 minutes
D. 490 minutes
E. 980 minutes

Kudos for a correct solution.

Diameter = 14
Height = 20

Volume = π*r^2*h = π (14/2)^2 * 20 = 980π

Total Time = Capacity to be filled / rate = (980π/2) / π = 490 Minutes

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A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Jul 2015, 05:53
R * T = W
diameter = 14
height = 20

$$\pi * t = \frac{1}{2}*\frac{14}{2}*20*\pi$$
Thus, D. 490 minutes

Thanks,
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Joined: 28 Jun 2015
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Concentration: Finance
GPA: 3.5
Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Jul 2015, 08:40
cylinder, r=7, h = 20.
volume = (pi) (7^2) (20) = 980(pi)
half-full = 490(pi).
Time taken = 490*1 = 490 mins.
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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Jul 2015, 09:29
1
Volume of cylinder=pi×49×20
=980pi
1/2 full so 490pi

490pi× 1min/pi
=490 mins

D. 490 minutes
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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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03 Jul 2015, 08:03
volume = pi *r^2*h = 980 pi

Required time = half volume / pi = 490 pi /pi = 490

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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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04 Jul 2015, 11:35
Option D is correct
Diameter = 14
Height = 20

Volume = π*r^2*h = π (14/2)^2 * 20 = 980π

Total Time = (Volume/2)/ rate = (980π/2) / π = 490 Minutes
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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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04 Jul 2015, 12:19
Bunuel wrote:
A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill $$\pi$$ cubic meters of the tank every minute. How long will it take the water truck to fill the water tank from empty to half-full?

A. 140 minutes
B. 245 minutes
C. 280 minutes
D. 490 minutes
E. 980 minutes

Kudos for a correct solution.

Radius of the base of the right circular cylinder = r= 14/2=7 m
Height =h=20m

Volume = V = $$\pi*r^2*h$$ = $$\pi*49*20$$

Thus total time for filling half the quantity of cylinder = $$\frac{V}{2}*\frac{1}{\pi}$$= 490 minutes. Thus D is the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 52360
A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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06 Jul 2015, 06:14
Bunuel wrote:
A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill $$\pi$$ cubic meters of the tank every minute. How long will it take the water truck to fill the water tank from empty to half-full?

A. 140 minutes
B. 245 minutes
C. 280 minutes
D. 490 minutes
E. 980 minutes

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

First find the volume of the cylindrical tank:

$$V = \pi r^2 * h = \pi (7)^2 * 20 = 980\pi$$

If the water truck can fill $$\pi$$ cubic meters of the tank every minute, it will take 980 minutes to fill the tank completely; therefore, it will take 980/2 = 490 minutes to fill the tank halfway. This is equal to 8 hours and 10 minutes.

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Joined: 04 Jun 2016
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A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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17 Jul 2016, 03:11
Bunuel wrote:
A cylindrical water tank has a diameter of 14 meters and a height of 20 meters. A water truck can fill $$\pi$$ cubic meters of the tank every minute. How long will it take the water truck to fill the water tank from empty to half-full?

A. 140 minutes
B. 245 minutes
C. 280 minutes
D. 490 minutes
E. 980 minutes

Kudos for a correct solution.

Volume of the tank = $$\pi* r^2*h=\pi *7^2*20=980\pi$$

We need to fill the HALF TANK =$$\frac{980\pi}{2}$$=$$490\pi$$
Rate*Time=Work
$$\pi$$ * TIME=490$$\pi$$
TIME = $$\frac{490\pi}{\pi}$$=490 minutes
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Re: A cylindrical water tank has a diameter of 14 meters and a height of  [#permalink]

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02 Aug 2018, 08:56
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Re: A cylindrical water tank has a diameter of 14 meters and a height of &nbs [#permalink] 02 Aug 2018, 08:56
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