Question

A circle with radius \pink{6}6start color #ff00af, 6, end color #ff00af has a sector with a central angle of \purple{\dfrac{11}{6}\pi} 611​ πstart color #9d38bd, start fraction, 11, divided by, 6, end fraction, pi, end color #9d38bd radians .What is the area of the sector?Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answer 1

`33\pi \:Square \:Units\\103.62 \:Square \:Units (In \: Decimal)`

Explanation:

Radius of the Circle = 6

Sectoral Angle =
`(11)/(6)\pi`

`\text{Area of a Sector=}(\theta)/(2\pi) X \pi r^2\\\theta=(11)/(6)\pi, r=6\\Therefore:\\Area=((11)/(6)\pi)/(2\pi) X \pi *6^2\\=(11)/(12)\pi X 36\\=33\pi`

`If\: \pi=3.14\\Area=33*3.14=103.62\:Square \:Units`