Find the length of the arc that subtends an angle of measure 70 degrees on a circle of diameter 15 centimeters.
22.5
35pi/12 cm
To find the length of the arc that subtends an angle of measure 70 degrees on a circle, we need to use the formula:
Arc Length = (Angle / 360) × (2π × Radius)
In this case, we are given the diameter of the circle, which is 15 centimeters. The radius is half of the diameter, so the radius would be 15/2 = 7.5 centimeters.
Now we can substitute the values into the formula:
Arc Length = (70 / 360) × (2π × 7.5)
First, we calculate (70 / 360):
Arc Length = (0.1944) × (2π × 7.5)
Next, we calculate (2π × 7.5):
Arc Length = (0.1944) × (47.1239)
Finally, we calculate the arc length:
Arc Length = 9.1550 centimeters
Therefore, the length of the arc that subtends an angle of measure 70 degrees on a circle of diameter 15 centimeters is approximately 9.1550 centimeters.
circumference = pi D = 15 pi
circumference /360 = arc length/70
so
arc length = 15 pi (7/36)