Question

1. A circular swimming pool has a diameter of 60 feet, and is surrounded by a concrete sidewalk that is 5 feet wide. What is the area of the sidewalk? Round to the nearest square foot.
Correct area of the pool and surrounding sidewalk: 4 points
Correct area of the pool water surface: 3 points
Correct area of the side walk: 1 point
Sentences explaining the process used:

Answer 1

We first calculate the area of the entire pool and the side walk.

Given that the pool has a diameter of 60 feet and that the side walk surrounds the pool with a width of 5 feet. This means that the diameter of the entire pool and the side walk is 60 + 5 + 5 = 70 feet and the radius is 70 / 2 = 35 feet

Thus the area of the entire pool and the side walk is obtained as follows:

$Area=\pi r^2 \\ \\ =\pi(35)^2=1,225\pi\ square\ feet$

Given that the pool has a diameter of 60 feet, this means that the radius of the pool is 30 feet.

Thus the area of the pool is given by:

$Area_{pool}=\pi r^2 \\ \\ =\pi(30)^2=900\pi\ square\ feet$

Therefore, the area of the sidewark is the area of the entire pool and side walk minus the area of the pool, this is given by:

$Area_{side walk}=1,225\pi-900\pi \\ \\ =325\pi=1,021 \ square\ feet.$