Thursday, September 15, 2011

A water tank with a height of 3.6 meters and a diameter of 1.8m has a capacity of 2,000 liters. After a few days of rain the tank is halfway...

There is something missing from this question and it has not been setup correctly. 


Density is a ratio of mass to the volume of a substance. That is,


density = mass of the substance / volume of the substance


In this question, we are given the dimensions of a cylindrical tank and its capacity. We are not given the mass of water it can hold. All the given dimensions are for length and volume and not mass. In absence of that information, density cannot be calculated.


Also, the volume of the tank has some issues. For example, the volume of the tank, as per the given dimensions, is:


volume = `pi` r^2 h = `pi` (1.8 /2)^2  x 3.6 = 9.156 m^3 = 9,156 L


With the given dimensions, the volume of the tank is over 9000 l, yet the question states it can hold only 2000 l of water.


Also, the information about the half filled tank during rain is not useful.


Thus, in absence of information about mass and clarity with volumetric data, density cannot be calculated. 


If instead the question stated that the tank with the given dimensions can hold 2000 kg of water, then density could have been calculated as:


density = 2000 kg / 9156 l = 0.22 kg/l (which is very less compared to the actual density of water)


 Hope this helps. 

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