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When a cylindrical tank is filled with water at a rate of 22

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When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post Updated on: 23 Sep 2013, 06:58
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When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

Had lots of trouble with this. i know the answer now but do not understand WHY... an elementary explanation is much appreciated.

Originally posted by Monyberumen on 23 Sep 2013, 06:45.
Last edited by Bunuel on 23 Sep 2013, 06:58, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 23 Sep 2013, 07:04
Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

Had lots of trouble with this. i know the answer now but do not understand WHY... an elementary explanation is much appreciated.


We are basically told that a cylinder with a height of 0.7 (7/10) meters has the volume of 22 cubic meters.

\(volume_{cylinder}=\pi{r^2}h=22\) --> \(\pi{\approx{\frac{22}{7}}}\) --> \(\frac{22}{7}*r^2*\frac{7}{10}=22\) --> \(r=\sqrt{10}\).

Answer: B.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #3 and 7. Thank you.
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 14 Jan 2015, 15:11
Hmmm, why is 0.7 the height..? Shouldn't 0.7 be multiplied with an unknown, as we don't know how many times the water will rise by 0.7?
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When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 14 Jan 2015, 15:13
Also, with the same logic, why is the capacity 22?

Is it perhaps that since we are not told about how long this rate will be filling in the tank, we can assume that with these numbers it will be totally full?
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 14 Jan 2015, 17:29
Hi pacifist85,

Imagine if we took a big cylinder and broke it into small "sections"; we'd just have a bunch of smaller cylinders that all had the same radius.

Here, we're given information about what happens in 1 HOUR: 22 cubic meters of water enter and the water level rises 0.7 meters.

From this data, the easiest thing to do is say that we have a "section" that is 0.7 meters high; in 1 hour that section will be FILLED by 22 cubic meters of water.

Next, we need the formula for Volume of a Cylinder:

V = pi(R^2)(H)

We have the Volume (22 cubic meters) and the Height (0.7 meters)...

22 = pi(R^2)(0.7)

At this point, the "math" would get pretty ugly, BUT the answer choices (and a little estimation) provide us with a way to avoid a lot of the math...

pi = about 3.14
.7(pi) = about 2.2

22 = 2.2(R^2)
10 = R^2
\sqrt{10} = R

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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 19 Jun 2015, 08:40
use the units to solve.

22 (m^3/hr) / .7 (m/hr) = (slighty over) ~30 m^2 = pi x r^2 * surface area of the rising water AND area of the cylinder

r= sqrt(~30/pi) = sqrt ( 10) * assume slighty over 3 is pi and use the above area equation to solve for approximate value of radius.
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 28 May 2017, 11:34
Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

Had lots of trouble with this. i know the answer now but do not understand WHY... an elementary explanation is much appreciated.


We can simply inspect the tube after one hour to determine the radius since the radius of the tube won't change over time. We know that the amount of water in the tube is equal to 22, so we can set it equal to the formula for the volume of a cylidner (piR^2H). Since the height rises by 0.7m/hr, we can set the height of the tube equal to its height after an hour.

22 = pi*r^2*H
22 = pi*r^2(7/10)
10 = r^2
\sqrt{10} = r
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 19 Apr 2018, 14:35
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Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10



Let's examine what occurs in a 1-hour period

The volume of water increases by 22 cubic meters.
The height of the water increases by 0.7 meters.

So, we need to find the radius of a 0.7 meter high cylinder that has a volume of 22 cubic meters.

Volume = (pi)(radius²)(height)
22 = (pi)(radius²)(0.7)

IMPORTANT: notice that (pi)(0.7) = approximately 2.2


So, we get: 22 ≈ (2.2)(radius²)
Divide both sides by 2.2: 10 ≈ radius²
Solve: radius ≈ √10

Answer: B

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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 02 Jun 2019, 11:33
Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

Had lots of trouble with this. i know the answer now but do not understand WHY... an elementary explanation is much appreciated.


in 1 hr
vol= 22 m3
and h= 0.7
so
22=22/7*r^2*7/10
r=√10
IMO B
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When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 02 Jun 2019, 14:19
The filling rates are given... Which makes it little difficult to interpret the situation.
Instead taking account of the rates just take a fixed time (says one hour) to make situation easy to understand.
In 1 hours the volume filled is 22 cubic m
And the height of this filled volume is 0.7 m
And now all you need to do is calculate the radius of cylinder or the volume filled (both of which are same)
V = πR²H
22 = π*R²*0.7
(22/7)*10 =π *R²
R² = 10
R = √10
IMO B

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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 25 Aug 2019, 19:01
Monyberumen wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10




We can let r = the radius of the tank, in meters. We know that the volume of the “slice” of the cylindrical tank that is filled in one hour is 22 cubic meters. We also know that the formula for the volume of that cylindrical “slice” is π x r^2 x .0.7, and we can create the equation:

π x r^2 x 0.7 = 22

Now let’s use 22/7 as the approximation for π:

22/7 x r^2 x 0.7 = 22

22 x r^2 x 0.1 = 22

r^2 x 0.1 = 1

r^2 = 10

r = √10

Answer: B
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Re: When a cylindrical tank is filled with water at a rate of 22  [#permalink]

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New post 08 Sep 2019, 01:54
To make it easier, assume the height of the cylinder to be 0.7 m, and he volume to be 22, as stated in the question.

Plug these values in the volume of cylinder formula (\(πr^2h\)) to get the value of r has 10^(-1/2)
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Re: When a cylindrical tank is filled with water at a rate of 22   [#permalink] 08 Sep 2019, 01:54
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