In the circle above, with centre O and radius 7 cm. Find the length of the arc AB, when < AOB = 57°.

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.