A circular fountain has a diameter of 12 feet. A 2-foot wide path surrounds the fountain. What is the total area of the fountain and the path around it?
radius=6+2
areatotal=pi*8^2
To find the total area of the fountain and the path around it, we need to calculate the individual areas of the fountain and the path, and then add them together.
First, let's find the area of the fountain itself. The fountain is circular, and we know its diameter is 12 feet. The formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Since the diameter is given, we can find the radius by dividing the diameter by 2:
r = 12 ft / 2 = 6 ft
Now let's compute the area of the fountain:
A_fountain = πr^2 = π * (6 ft)^2
Next, we need to calculate the area of the path. The path surrounds the fountain with a width of 2 feet. Since the path extends equally in all directions around the fountain, the diameter of the entire area (fountain + path) will be increased by 2 feet on each side. Therefore, the diameter of the entire area will be:
D_total = 12 ft + 2 ft + 2 ft = 16 ft
Again, we can find the radius by dividing the diameter by 2:
r_total = 16 ft / 2 = 8 ft
Now, let's calculate the area of the entire circular area (fountain + path):
A_total = πr_total^2 = π * (8 ft)^2
Finally, to find the area of the path, we subtract the area of the fountain from the area of the entire circular area:
A_path = A_total - A_fountain
Now we can calculate the values:
A_fountain = π * (6 ft)^2
A_total = π * (8 ft)^2
A_path = A_total - A_fountain
After calculating the values, we can sum the area of the fountain and the path to get the total area:
Total area = A_fountain + A_path
Let's do the calculations: