Question

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?

Answer 1

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%`.

Answer 2

`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`