Answer :
Answer:
the area of the sector with a central angle of 11/6π radians is equal to [tex]998.25\pi^3[/tex]
Step-by-step explanation:
The area A of the entire circle is given by:
[tex]A=\pi *r^{2}[/tex]
Where r is the radius of the circle. So the area of a circle with radius [tex]33\pi[/tex] is:
[tex]A=\pi *(33\pi)^2=1089\pi^3[/tex]
Additionally an entire circle has a central angle of [tex]2\pi[/tex] radians.
So, we can calculate the area of a sector using the rule of three in which we know that [tex]2\pi[/tex] radians has an Area of [tex]1089\pi^3[/tex] then what is the area of the sector with a central angle of 11/6π radians as:
[tex]1089\pi^3 ------------2\pi\\ x--------------\frac{11}{6}\pi[/tex]
Where x is the area of the sector with a central angle of 11/6π radians.
Finally, solving for x, we get:
[tex]x=\frac{11/6\pi *1089\pi^3 }{2\pi } =998.25\pi^3[/tex]
So, the area of the sector with a central angle of 11/6π radians is equal to [tex]998.25\pi^3[/tex]