Question

the tank shown below has a volume of 0.45 m³. if the volumetric flowrate from the faucet is equal to 198.7 cm³/sec, how long (in minutes) will it take to fill the tank completely? the tank is empty at the start (time = 0). report your answer to two decimal places.

Explanation:

Step1: Convert volume units

First, convert the volume of the tank from $m^{3}$ to $cm^{3}$. Since $1m^{3}=10^{6}cm^{3}$, the volume of the tank $V = 0.45m^{3}=0.45\times10^{6}cm^{3}=450000cm^{3}$.

Step2: Use the flow - rate formula

The flow - rate formula is $Q=\frac{V}{t}$, where $Q$ is the volumetric flow - rate, $V$ is the volume, and $t$ is the time. We want to find $t$, so $t=\frac{V}{Q}$. Given $Q = 198.7cm^{3}/s$, then $t=\frac{450000cm^{3}}{198.7cm^{3}/s}\approx2264.73s$.

Step3: Convert time units

Convert the time from seconds to minutes. Since $1$ minute $ = 60$ seconds, then $t=\frac{2264.73s}{60s/min}\approx37.75min$.

Answer:

$37.75$