In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.
Question 1 Report
In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.
Answer Details
The length of an arc in a circle can be found using the formula:
Arc Length = (Angle Measure / 360) * (Circumference of Circle)
The circumference of the circle can be found using the formula:
Circumference = 2 * pi * radius
So, first find the circumference of the circle:
Circumference = 2 * pi * 7 = 14 * pi
Next, find the angle measure in degrees in terms of pi:
57 degrees = 57 * pi / 180 radians
Now, plug in the values into the formula for arc length:
Arc Length = (57 * pi / 180) * (14 * pi) = (57 / 360) * (14 * pi) = (57 / 360) * (43.98) = 43.98 * (57 / 360) = (43.98 * 57) / 360 = 2493.86 / 360 = 6.97 cm
So, the length of the arc AB is 6.97 cm.
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