A circle has a circumference of 12π feet (ft). An arc, x, in this circle has a central angle of 330∘. Rounded to the nearest foot, what is the length of x ?
Q. A circle has a circumference of 12π feet (ft). An arc, x, in this circle has a central angle of 330∘. Rounded to the nearest foot, what is the length of x ?
Find Radius of Circle: Find the radius of the circle using the circumference.The formula for the circumference of a circle is C=2πr, where C is the circumference and r is the radius.Given C=12π, we can solve for r:12π=2πrDivide both sides by 2π to isolate r:r=2π12πr=6
Calculate Length of Arc: Calculate the length of the arc x.The formula for the length of an arc (s) with a central angle (θ) in degrees in a circle of radius r is s=360θ×2×π×r.Given θ=330 degrees and r=6 feet, we can plug these values into the formula:s=360330×2×π×6s=1211×2×π×6s=11×π×126s0s1
Round Length of Arc: Round the length of the arc to the nearest foot.Since π is approximately 3.14159, we can estimate the length of the arc:s≈5.5×3.14159s≈17.278Rounded to the nearest foot, the length of the arc x is approximately 17 feet.
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