A circle with a radius of 6 has a sector with a central angle of 11/6pi radians

what is the area of the sector?

33pi

Step-by-step explanation:

11pi/6 is almost 2pi, the entire circle

the entire circle's area = pi(r)^2 = pi(6)^2 = pi(36) = 36pi

But the sector with angle 11pi/6 is 11/12 th's of a circle's area

11/12 x 36pi = 33pi = area of the sector

33pi = 33(3.14159) = 103.67 = Area rounded to 2 decimal places

If you wanted to know the part of the circumference subtended by the angle, the formula is just the angle times the radius or 11pi/6 x 6 = 11pi   had it been 12pi/6 or 2pi, the circumference would have been pid or pi times the diameter,  12pi.   11pi is almost all of the circumference.  

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33π units²

Step-by-step explanation:

Find the area of the entire circle first.  It is A = πr².  Here, that comes to

A = π(6 units)^2

We are interested only in the area of the sector defined by central angle (11/6)π.  We form a fraction with this (11/6)π in the numerator and 2π in the denominator, and then multiply the area of the full circle by this fraction:

  (11/6)π

* 36π units²

      2π

This reduces to 33π units²