A circle with a radius 6 has a sector with a central angle of 11/6 pi radians. What is the area of the sector?

Question

Either enter an exact answer in terms of πpi or use 3.143, point, 14 for πpi and enter your answer as a decimal.

(3.14 instead of pi also works)

(THANKS)

Answer 1

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.

pi=3.14159....

Answer 2

First let's remember that a sector will be part of the total area of the circle and we know that the formula for the area of the circle is A = π r²

So this will give us the whole circle area.

If we want to find the fraction of the circle that has an angle of 11/6 π then we have to put this angle over the angle of the total circle which is 360° or 2 π.

Once we find the fraction of the sector to the whole circle, we can multiply the fraction times the whole area.

To set up the fraction we can us ( (11/6)π)/(2π)).

Now you can use this fraction and the value for r to find the area of the sector.

I hope this helped.

Answer 3

A = (0.5)r² θ

A = (0.5)(6)²(11π/6)