SOLUTION: A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. A concrete sidewalk 5 feet wide encircles the pool, and the

Algebra ->  Surface-area -> SOLUTION: A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. A concrete sidewalk 5 feet wide encircles the pool, and the      Log On


   

Question 1057369: A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. A concrete sidewalk 5 feet wide encircles the pool, and the rest of the region is grass, as shown in the figure below. (I added a link to the picture used in the problem. https://www.dropbox.com/s/jxc7syj05xb0lrh/8-1-023.gif?dl=0 )
Find the surface area of the water
Find the area of the concrete sidewalk
Find the area of the grass
Some of these I believe I can solve (sidewalk and grass area), but the surface area is something I have not done in about 15 years, and I am very rusty with it.
Found 2 solutions by Alan3354, solve_for_x:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A circular swimming pool has diameter 50 feet and is centered in a fenced-in square region measuring 80 feet by 80 feet. A concrete sidewalk 5 feet wide encircles the pool, and the rest of the region is grass, as shown in the figure below. (I added a link to the picture used in the problem. https://www.dropbox.com/s/jxc7syj05xb0lrh/8-1-023.gif?dl=0 )
Find the surface area of the water
-- Area = pi*r^2 = pi*25^2 = 625pi sq feet.
----
Find the area of the concrete sidewalk
r to the outside of the concrete = 25+5 = 30 feet
Area = pi*30^2 - area of the water
= 900pi - 625pi sq feet = 225pi sq feet
-----
Find the area of the grass
= 80*80 - the other 2 areas
= 6400 - 900pi sq ft.

Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
It is easiest to start with the water surface and work your way outward.

The surface area of the water is just the area of the circle: pi%2Ad%5E2%2F4

Since the diameter is d = 50 ft, the surface area is pi%2A50%5E2%2F4 = 1963.5 sq. ft

The 5 ft sidewalk around the perimeter of the pool makes a larger circle, with a diameter of 60 ft.

Find the area of this larger circle, and subtract the area of the water surface that was
calculated above to get the area of the sidewalk:

Area of sidewalk = pi%2A60%5E2%2F4+-+pi%2A50%5E2%2F4 = 2827.43 - 1963.50 = 863.93 sq. ft.

Finally, the area of the grass is the difference between the area of the fenced region, minus the area of the larger circle (2827.43 sq. ft):

Area of grass = (80 * 80) - 2827.43 = 3,572.57 sq. ft.