At the park there is a pool shaped like a circle with radius 11yd. A ring-shaped path goes around the pool. Its width is 6yd.
6yd
11yd
We are going to give a new layer of coating to the path. If one gallon of coating can cover 8yd2, how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. (Use the value 3.14 for π.)
Yo are you dense
Area of the walkway = total area - center area
Note: total area is the largest circle... it's radius is found by adding the radius of the inside circle 11 to the width of the walkway
remember that area is (pi)(r)(r)
Area of walkway = (3.14)(11 + 6)(11+6) - (3.14)(6)(6)
and you finish it off : )
To find the area of the ring-shaped path, we need to find the area of the outer circle and subtract the area of the inner circle.
First, let's find the area of the outer circle. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius of the outer circle is 11yd. So, the area of the outer circle is:
A_outer = π * (11yd)^2
A_outer = 3.14 * (11yd)^2
A_outer = 3.14 * 121yd^2
A_outer ≈ 380.14yd^2
Next, let's find the area of the inner circle. The radius of the inner circle is the radius of the outer circle minus the width of the path, which is 6yd. So, the radius of the inner circle is:
r_inner = 11yd - 6yd
r_inner = 5yd
Using the same formula, we can find the area of the inner circle:
A_inner = π * (5yd)^2
A_inner = 3.14 * 25yd^2
A_inner ≈ 78.5yd^2
Now, we can find the area of the ring-shaped path by subtracting the area of the inner circle from the area of the outer circle:
A_path = A_outer - A_inner
A_path ≈ 380.14yd^2 - 78.5yd^2
A_path ≈ 301.64yd^2
Given that one gallon of coating can cover 8yd^2, we can now calculate the number of gallons needed:
Number of gallons = A_path / (8yd^2/gallon)
Number of gallons ≈ 301.64yd^2 / (8yd^2/gallon)
Number of gallons ≈ 301.64yd^2 * (gallon/8yd^2)
Number of gallons ≈ 37.705 gallons
Since the number of gallons must be a whole number, we round up to the nearest whole gallon.
Therefore, you will need approximately 38 gallons of coating to cover the ring-shaped path.