Bollough Junior High is planning to build a new circular fountain in the courtyard. One contractor has suggested building a fountain that has a diameter of 40 feet. Another contractor has suggested building a fountain that has a diameter of 50 feet. How many square feet greater is the area of the second fountain than the area of the first fountain?
pi ( Rbig^2 - Rsmall^2)
= 3.14159 ( 625 - 400)
=
since the radii are 20 and 25 ft, you want
π(25^2 - 20^2) = 225π ft^2
To find the difference in area between the two fountains, we need to calculate the area of each fountain and then subtract the smaller area from the larger one.
First, let's calculate the area of the fountain with a diameter of 40 feet. The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius. Since the diameter is 40 feet, the radius is half of that, which is 40 / 2 = 20 feet. Therefore, the area of the first fountain is A1 = π * (20^2).
Next, let's calculate the area of the fountain with a diameter of 50 feet. Again, the radius is half of the diameter, so the radius is 50 / 2 = 25 feet. The area of the second fountain is A2 = π * (25^2).
Now, we can find the difference in area by subtracting A1 from A2: A2 - A1.
Using approximation, the value of π is approximately 3.14, but for more accuracy, you can use more decimal places, such as 3.14159.
Calculating the areas:
A1 = 3.14 * (20^2)
A2 = 3.14 * (25^2)
Finally, subtract A1 from A2 to find the difference in square feet:
Area Difference = A2 - A1
Now, insert the respective values and calculate the difference to find out how many square feet greater the area of the second fountain is compared to the first one.