To determine how long it will take to fill the cylindrical tank, we first need to calculate the total volume of the tank, and then we can find out how much more water is needed after accounting for the initial amount.
Step 1: Calculate the volume of the cylindrical tank.
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
From the problem, we know the diameter of the tank is 6 feet, which means the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{6 \text{ feet}}{2} = 3 \text{ feet} \]
The height \( h \) of the tank is given as 18 feet.
Now, we can calculate the volume:
\[ V = \pi (3 \text{ feet})^2 (18 \text{ feet}) = \pi \times 9 \text{ feet}^2 \times 18 \text{ feet} = 162\pi \text{ cubic feet} \]
Using the value of \( \pi \approx 3.14 \):
\[ V \approx 162 \times 3.14 \approx 508.68 \text{ cubic feet} \]
So, the total volume of the tank is approximately 508.68 cubic feet.
Step 2: Calculate the remaining volume to fill the tank.
The tank currently contains 60 cubic feet of water. Therefore, the volume of water needed to fill the tank is:
\[ \text{Remaining volume} = 508.68 \text{ cubic feet} - 60 \text{ cubic feet} \approx 448.68 \text{ cubic feet} \]
Step 3: Calculate the time required to fill the remaining volume.
The tank is being filled at a rate of 10 cubic feet per minute. Thus, the time \( t \) in minutes to fill the remaining volume is:
\[ t = \frac{\text{Remaining volume}}{\text{Rate}} = \frac{448.68 \text{ cubic feet}}{10 \text{ cubic feet per minute}} = 44.868 \text{ minutes} \]
Step 4: Round to the nearest minute.
Rounding 44.868 minutes to the nearest minute gives:
\[ t \approx 45 \text{ minutes} \]
Thus, it will take approximately 45 minutes to fill the tank.
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