Answer:
The area of the sector is 33[tex]\pi[/tex].
Explanation:
A sector is a part of a circle that is formed by two radii (which forms a central angle), and an arc. The area of a sector (in radians) is given by:
= (θ ÷ [tex]2\pi[/tex]) × [tex]\pi r^{2}[/tex]
where: θ is the central angle of the sector and r is the radius of the circle of which the sector is a part.
Area of a circle = [tex]\pi r^{2}[/tex]. But the area of the circles was given to be 36[tex]\pi[/tex].
Area of the sector = (θ ÷ [tex]2\pi[/tex]) × area of the circle
= (θ ÷ [tex]2\pi[/tex]) ×36[tex]\pi[/tex]
θ has been given to be [tex]\frac{11}{6}[/tex][tex]\pi[/tex].
Therefore;
Area of the sector = ([tex]\frac{11}{6}[/tex][tex]\pi[/tex] ÷ [tex]2\pi[/tex]) ×36[tex]\pi[/tex]
= [tex]\frac{11}{12}[/tex] × 36[tex]\pi[/tex]
= 11 × 3[tex]\pi[/tex]
= 33[tex]\pi[/tex]
The area of the sector is 33[tex]\pi[/tex].
