The Correct Answer and Explanation is:
The approximate area of the walkway is 179 square feet.
To solve this problem, we need to find the area of the walkway, which is the space between two circles. This shape is called an annulus. The strategy is to calculate the area of the large outer circle, which includes both the fountain and the walkway, and then subtract the area of the small inner circle, which is just the fountain. The remaining area will be that of the walkway.
First, let’s find the dimensions of the inner circle, the fountain. The problem states its diameter is 16 feet. The radius of a circle is half of its diameter, so the fountain’s radius is 16 feet divided by 2, which equals 8 feet. The formula for the area of a circle is A = πr². Using this, the area of the fountain is π multiplied by (8 feet)², resulting in 64π square feet.
Next, we determine the dimensions of the large outer circle. This circle’s radius is the fountain’s radius plus the width of the walkway. The walkway is 3 feet wide. Therefore, the radius of the large circle is 8 feet plus 3 feet, which is 11 feet. Using the same area formula, the area of the large circle is π multiplied by (11 feet)², which equals 121π square feet.
Finally, to find the area of the walkway, we subtract the area of the inner circle from the area of the outer circle. This calculation is 121π minus 64π, which gives us an exact area of 57π square feet for the walkway.
To get an approximate numerical value, we use the approximation of π as 3.14. Multiplying 57 by 3.14 gives us 178.98. Rounding this to the nearest whole number, we get 179 square feet as the approximate area of the walkway.
