The bags of stones Mr. Townes will need are 20 bags.
Given:
The radius of the circular garden is 7 feet.
The width of the circular path around the park is 2 feet.
To find:
The bags of stones needed by Mr. Townes to cover the garden path.
Solution:
The radius of the circular garden = 7 ft
The width of the circular path around the park = 2 ft
The radius of the inner circle = r = 7 ft
The radius of the outer circle = r' = 7 ft + 2 ft = 9 ft
The area of the inner circle = A
[tex]A=\pi r^2\\\\A=3.14\times (7 ft)^2=153.94 ft^2[/tex]
The area of the outer circle = A'
[tex]A'=\pi r'^2\\\\A'=3.14\times (9 ft)^2=254.47ft^2[/tex]
The area of the circular garden path = C
[tex]C = A' - A \\\\= 254.47ft^2-153.94 ft^2 =100.53ft^2[/tex]
Mr. Townes needs 1 bag of stones for every 5 square feet of a path, then for 100.53 square feet he will need:
[tex]=\frac{1}{5}\times 100.53=20.106bags\approx 20bags[/tex]
The bags of stones Mr. Townes will need are 20 bags.
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