2. A circle has a radius of 10 centimeters. Find the length, in centimeters, of the arc
intercepted by a central angle of 100 degree.
(A) 50pi/9 (B) 100pi/9 (C) 500pi/9 (D) 18pi/5 (E) None of the above.
C = pi*dia = pi*20 = 20pi cm.
Arc = (100/360) * 20pi = 5.6pi = 50pi/9
(E) none of the above
To find the length of the arc intercepted by a central angle, we can use the formula:
Arc Length = (Central Angle / 360) * (2 * π * Radius)
In this case, the radius of the circle is given as 10 centimeters and the central angle is 100 degrees.
Plugging in these values into the formula, we have:
Arc Length = (100 / 360) * (2 * π * 10)
Simplifying further, we get:
Arc Length = (10/36) * (20π)
Arc Length = (5/18) * (20π)
Arc Length = (100π/18)
Now, we can simplify it further to get the answer in the required form:
Arc Length = (50π/9)
Therefore, the length of the arc intercepted by a central angle of 100 degrees on a circle with a radius of 10 centimeters is (50π/9).
Hence, the correct answer choice is (A) 50π/9.