Answer:
Approx 4.37 minute
Step-by-step explanation:
To determine how many minutes it will take to fill the empty gas tank, we'll first need to calculate the volume of the cylindrical tank and then divide that volume by the rate at which gas is being poured in.
### Step 1: Calculate the Volume of the Cylindrical Tank
The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or length) of the cylinder.
Given:
- The diameter of the tank is 1.6 ft, so the radius \( r \) is half of the diameter:
\[ r = \frac{1.6 \, \text{ft}}{2} = 0.8 \, \text{ft} \]
- The height (length) of the tank \( h \) is 5 ft.
Now, plug these values into the formula:
\[ V = \pi (0.8 \, \text{ft})^2 (5 \, \text{ft}) \]
\[ V = \pi (0.64 \, \text{ft}^2) (5 \, \text{ft}) \]
\[ V = \pi (3.2 \, \text{ft}^3) \]
\[ V \approx 3.2 \times 3.14159 \]
\[ V \approx 10.053 \, \text{ft}^3 \]
### Step 2: Calculate the Time to Fill the Tank
Given the rate at which gas is poured into the tank is 2.3 ft³ per minute, we can find the time \( t \) it takes to fill the tank by dividing the volume of the tank by the rate:
\[ t = \frac{V}{\text{rate}} \]
\[ t = \frac{10.053 \, \text{ft}^3}{2.3 \, \text{ft}^3/\text{minute}} \]
\[ t \approx 4.37 \, \text{minutes} \]
Therefore, it will take approximately 4.37 minutes to fill the empty gas tank.