Final answer:
To calculate the surface area of the inner pond of a circular fountain with an overall diameter of 10 meters and an inner pond 2 meters from the outer edge, you find the radius of the inner pond and use the formula for the area of a circle.
Step-by-step explanation:
Calculating the surface area of the inner pond requires information about the overall size of the fountain and the distance from the inner to the outer pond. Since the fountain is circular in shape and the inner pond is 2 meters away from the outer edge, knowing the diameter or radius of the full fountain can help us determine the radius of the inner pond.
The question states that the fountain measures 10 meters across, which implies that this is the diameter of the entire fountain. To find the diameter of the inner pond, we would subtract the distance between the inner and outer ponds, multiplied by 2 (since it needs to be subtracted from both sides), from the total diameter of the fountain.
Surface area of inner pond: π × (radius of inner pond)^2
Given diameter of fountain: 10 meters
Distance from outer to inner pond: 2 meters on each side
Diameter of inner pond = Diameter of fountain - 2 × (distance from outer to inner pond)
Diameter of inner pond = 10 meters - 2 × 2 meters
Diameter of inner pond = 10 meters - 4 meters
Diameter of inner pond = 6 meters
Radius of inner pond = Diameter of inner pond / 2
Radius of inner pond = 6 meters / 2
Radius of inner pond = 3 meters
Surface area of inner pond = π × (3 meters)^2
Surface area of inner pond = π × 9 square meters
Surface area of inner pond = 28.274 square meters (using π = 3.14159)