An advertisement states that a Roto-Sprinkler can water a cicular region with area 1000 ft^2. Find the diameter of this region to the nearest foot. Use pi = 3.14.
1000 = pi D^2/4
D^2 = 4000/pi
D = 35.69
which is 36 to the nearest foot
To find the diameter of the circular region, we need to use the formula for the area of a circle.
The formula for the area of a circle is:
A = πr^2
Where A is the area of the circle, π is approximately 3.14, and r is the radius of the circle.
In this case, we are given that the area of the circular region is 1000 ft^2. We need to find the diameter, but we can start by finding the radius.
Step 1: Use the formula for the area of the circle to find the radius.
1000 = πr^2
To isolate the radius, divide both sides of the equation by π:
1000/π = r^2
Step 2: Take the square root of both sides of the equation to find the radius.
√(1000/π) = r
Step 3: Evaluate the square root using approximately π = 3.14.
√(1000/3.14) ≈ r (Note: Use a calculator for the evaluation)
r ≈ 17.95 ft
Step 4: Finally, calculate the diameter by multiplying the radius by 2.
d = 2r
d ≈ 2 * 17.95 ≈ 35.90 ft
Therefore, the diameter of the circular region is approximately 35.90 feet. Rounding to the nearest foot, the diameter would be 36 feet.