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

Answer:

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

Step-by-step explanation:

Radius of the Circle = 6

Sectoral Angle =$\frac{11}{6}\pi$

$\text{Area of a Sector=}\dfrac{\theta}{2\pi} X \pi r^2\\\theta=\frac{11}{6}\pi, r=6\\Therefore:\\Area=\dfrac{\frac{11}{6}\pi}{2\pi} X \pi *6^2\\=\dfrac{11}{12}\pi X 36\\=33\pi$

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