The problem asks to calculate the surface area of a portion of a water tower modeled as a sphere with a diameter of 30 feet, to help estimate the amount of paint needed.

Step-by-step solution:

1. Identify the radius: Since the diameter of the sphere is given as 30 feet, the radius $r$ is half of that: $r = \frac{30}{2} = 15 \text{ feet}.$

2. Use the surface area formula for a sphere: The formula for the surface area of a full sphere is: $A = 4\pi r^2$ Plugging in the value of $r = 15$: $A = 4\pi (15)^2 = 4\pi \times 225 = 900\pi.$

3. Approximate using $\pi \approx 3.1416$: $A = 900 \times 3.1416 = 2827.43 \text{ square feet}.$

Thus, the surface area of the spherical portion of the water tower is approximately 2827 square feet.

Would you like more details or clarifications on this?

Here are some follow-up questions you might find interesting:

1. What is the volume of the entire water tower if it were a full sphere?
2. How much paint would be needed if one gallon covers 350 square feet?
3. What would the surface area be if the diameter were doubled?
4. How would the surface area change if only half the sphere is painted?
5. What is the relationship between surface area and volume for spheres?

Tip: When calculating areas involving circles or spheres, using an accurate approximation of $\pi$ (like 3.1416) can make a significant difference in the result.