To find out how many gallons of water can be treated at the plant at any one time, we first need to calculate the volume of one cylindrical tank and then find the total volume for three tanks.
Step 1: Calculate the volume of one 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 (or depth) of the cylinder.
Given:
- Radius \( r = 15 \) feet,
- Height \( h = 22 \) feet.
Now, substituting these values into the formula:
\[ V = \pi (15)^2 (22) \] \[ V = \pi (225) (22) = 4950\pi \text{ cubic feet} \]
Step 2: Calculate the total volume for three tanks
We have three tanks, so we multiply the volume of one tank by 3:
\[ \text{Total Volume} = 3 \times 4950\pi = 14850\pi \text{ cubic feet} \]
Step 3: Calculate the total volume in gallons
Since there are about 7.5 gallons in a cubic foot, we can find the total gallons:
\[ \text{Total Gallons} = 14850\pi \times 7.5 \]
First, we need to calculate \( 14850 \times 7.5 \):
\[ 14850 \times 7.5 = 111375 \]
Now, using \( \pi \approx 3.14 \):
\[ \text{Total Gallons} \approx 111375 \times 3.14 \approx 349,493.75 \]
Conclusion
We round 349,493.75 to the nearest whole number:
- Approximately \( 349,494 \) gallons.
Now let's express this in scientific notation:
\[ 349,494 \approx 3.49494 \times 10^5 \approx 3.5 \times 10^5 \]
Final Answer
The correct choice is:
A. \( 3.5 \times 10^5 \)