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# An empty cylindrical tank with a radius of 5 inches and a height of 10

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Math Expert
Joined: 02 Sep 2009
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An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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17 Jan 2019, 02:34
00:00

Difficulty:

55% (hard)

Question Stats:

77% (01:14) correct 23% (01:05) wrong based on 13 sessions

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An empty cylindrical tank with a radius of 5 inches and a height of 10 inches is filled with water at a rate of 75 cubic feet per second. Approximately how many seconds will it take for the tank to be full?

A 8

B 9

C 11

D 13

E 15

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Re: An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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17 Jan 2019, 05:42
Bunuel wrote:
An empty cylindrical tank with a radius of 5 inches and a height of 10 inches is filled with water at a rate of 75 cubic feet per second. Approximately how many seconds will it take for the tank to be full?

A 8

B 9

C 11

D 13

E 15

Bunuel :
the volume is given in inches and flow rate is given in ft ^3 per sec..
no conversion feet to inches given..
it seems that either flow rate is also in in^3 per sec
so answer would be 11 IMO C ..else if the flow rate is in ft^3 per sec then answer option is not given
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Re: An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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19 Jan 2019, 21:15
Bunuel wrote:
An empty cylindrical tank with a radius of 5 inches and a height of 10 inches is filled with water at a rate of 75 cubic feet per second. Approximately how many seconds will it take for the tank to be full?

A 8

B 9

C 11

D 13

E 15

Cylinder volume = 22/7* r^2 *h = 22/7*25*10

75 -------------- 1 sec
22/7*250-------(x) ?

x=( 22/7*250)/75
=220/21
=10.476
~11

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Re: An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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19 Jan 2019, 23:57
Bunuel wrote:
An empty cylindrical tank with a radius of 5 inches and a height of 10 inches is filled with water at a rate of 75 cubic feet per second. Approximately how many seconds will it take for the tank to be full?

A 8

B 9

C 11

D 13

E 15

Volume of the Cylindrical cube is $$π*5^2*10$$

Speed of water rushed into the tank is $$75 => 5^2*3$$

So time required is $$\frac{π*5^2*10}{5^2*3}=\frac{10π}{3} = \frac{10*22}{7*3}$$

Or, the time required is $$\frac{220}{21}$$ ~ $$11$$, Thus Answer must be (C) 11
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Re: An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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20 Jan 2019, 00:05
Abhishek009 wrote:
Bunuel wrote:
An empty cylindrical tank with a radius of 5 inches and a height of 10 inches is filled with water at a rate of 75 cubic feet per second. Approximately how many seconds will it take for the tank to be full?

A 8

B 9

C 11

D 13

E 15

Volume of the Cylindrical cube is $$π*5^2*10$$

Speed of water rushed into the tank is $$75 => 5^2*3$$

So time required is $$\frac{π*5^2*10}{5^2*3}=\frac{10π}{3} = \frac{10*22}{7*3}$$

Or, the time required is $$\frac{220}{21}$$ ~ $$11$$, Thus Answer must be (C) 11

Abhishek009

If you see the flow rate is given in cubic feet per second / ft^3 ; where as the dimensions of the tank are given in inches... dont you think that we need to convert feet to inches or vice versa so as to get exact time rate .. I had asked Bunuel similar doubt I am yet to get his response..
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Re: An empty cylindrical tank with a radius of 5 inches and a height of 10  [#permalink]

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20 Jan 2019, 00:18
Bunuel :
There seems to be some disparity in the question with respect to units, So if unit conversion is not considered:

Work = Volume of cylinder = pi*r^2*h = 22/7 * 25 * 10
Rate = 75 cubic feet/sec
Time = Work/Rate = 22*25*20/7*75 ~ 11
Re: An empty cylindrical tank with a radius of 5 inches and a height of 10   [#permalink] 20 Jan 2019, 00:18
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