Question

The gas tank of a truck is a cylinder 4.5ft long with a diameter of 2ft . At the gas station, a pump pours gas at the rate of 4ft^3 per minute. How many minutes does it take to fill the empty tank with that pump?

Answer 1

find the volume of the tank, to see how much gas in square feet it will take

Answer 2

\[
\text{cylinder_base} = \pi r^2 = \pi \cdot (2_{ft})^2 = 4\pi_{ft^2} \\
\text{volume_of_cylinder} = \text{base} \cdot \text{height} = 4\pi_{ft^2} \cdot 4.5_{ft} = 18\pi_{ft^3} \\
\]
Now, the ratio between the volume the pump could fill in a minute and the ratio of the volume of the gas tank gives us the minutes it would take to fill it. so:
\[
\text{pump_rate_per_minute} = (4_{ft^3/min})^3 = 16 \cdot 4 = 64_{ft^3/min} \\
\text{ratio} = \frac{ \text{pump_rate_per_minute} }{ \text{volume_of_cylinder} } = \frac{64_{ft^3/min}}{18\pi_{ft^3}} = 1.31_{min}
\]