An empty tank is filled with water at the rate of 200 cc per second. The dimensions of the tank are 2 m by 3 m by 4 m. What fraction of the tank is filled after two hours?

2 Answers
Feb 17, 2018

The answer is #3/50#.

Explanation:

First, let's find out how many cubic centimeters the tank can hold using dimensional analysis:

#(2cancel"m")/1xx(100"cm")/cancel"m"xx(3cancel"m")/1xx(100"cm")/cancel"m"xx(4cancel"m")/1xx(100"cm")/cancel"m"#

#200"cm"xx300"cm"xx400"cm"#

#24000000"cm"^3#

Next, let's convert the filling speed from #"cm"^3/"s"# to #"cm"^3/"hr"#:

#(200"cm"^3)/cancel"s"xx(60cancel"s")/(1cancel"min")xx(60cancel"min")/(1"hr")#

#(200"cm"^3*60*60)/(1"hr")#

#(720000"cm"^3)/"hr"#

Now, let's find out how many cubic centimeters were filled after two hours:

#(720000"cm"^3)/cancel"hr"*2cancel"hrs"#

#720000"cm"^3 *2#

#1440000"cm"^3#

Lastly, divide this number by the total capacity of the pool to find out what fraction of the pool is filled:

#(1440000cancel("cm"^3))/(24000000cancel("cm"^3))#

#(144cancel(0000))/(2400cancel(0000))#

#144/2400#

#12/200#

#3/50#

Three-fiftieths of the pool was filled after two hours, or #6%#.

Feb 17, 2018

#0.06# is filled after #2h#

Explanation:

First, least determine the volume of the tank:

#V= L*w*h = 2m*3m*4m = 24m^3#

We are given a flow rate in #cm^3//s#, so it would be nice to have the volume in the same volume units as the flow rate. I'm going to choose litres for volume. Using the conversion factor method we write:

#(200cm^3)/s * (1ml)/(1cm^3)*(1l)/(1000ml)=0.200 l//s#

To convert #m^3# to litres, we know that

#1l=1dm^3 = (0.1m)^3 = 0.001m^3#

#24m^3*(1l)/(0.001m^3)=24000l#

The volume of water that flows into the tank in #2h# is

#V_(water) = 0.200l/s*2h*(60m)/(1h)*(60s)/(1m) = 1440l#

Therefore, the fraction of the tank that is filled is:

#(1440l)/(24000l) = 0.06#