The fountain in the middle of a park is circular, with a diameter of 16 feet. There is a walkway that is 3 feet wide that goes around the fountain. What is the approximate area of the walkway?
A. 179 sq. ft.
B. 159 sq. ft.
C. 28 sq. ft.
D. 16 sq. ft.
The Correct Answer and Explanation is :
To find the area of the walkway, let’s break down the problem into two parts:
- Calculate the area of the fountain itself, which is a circle with a diameter of 16 feet. The radius (half the diameter) is therefore ( \frac{16}{2} = 8 ) feet. Using the formula for the area of a circle, ( A = \pi r^2 ), we can substitute the radius: [
A_{\text{fountain}} = \pi \times 8^2 = 64\pi
] - Calculate the area of the larger circle that includes both the fountain and the walkway. The walkway is 3 feet wide, so the radius of this larger circle is the radius of the fountain plus the width of the walkway: [
\text{New radius} = 8 + 3 = 11 \text{ feet}
] Using the area formula again, we calculate the area of the larger circle: [
A_{\text{fountain + walkway}} = \pi \times 11^2 = 121\pi
] - Calculate the area of the walkway by subtracting the area of the fountain from the area of the larger circle: [
A_{\text{walkway}} = A_{\text{fountain + walkway}} – A_{\text{fountain}} = 121\pi – 64\pi = 57\pi
] - Now, approximate the area by substituting ( \pi \approx 3.14 ): [
A_{\text{walkway}} \approx 57 \times 3.14 = 179.14 \text{ square feet}
]
Answer: The approximate area of the walkway is 179 square feet, so the correct answer is A. 179 sq. ft.
Explanation:
The key steps involved understanding that the walkway forms an “annular” (ring-like) region around the fountain. To find the area of this region, we needed the radius of both the inner (fountain) and outer (fountain plus walkway) circles. Calculating each circle’s area separately and subtracting them allowed us to isolate the walkway’s area.