Respuesta :
Answer:
[tex]\frac{27}{2} \pi[/tex] or [tex]13.5\pi[/tex]
Step-by-step explanation:
Recall the formula for the area of a circular sector: [tex]A = (\frac{x}{360}) r^2\pi[/tex], where x is the central angle of the sector and r is the radius of the circle.
Apply that, A simplifies to,
[tex]A = (\frac{135}{360} )6^2\pi =(\frac{3}{8} )36\pi =\frac{27}{2} \pi =13.5\pi[/tex]
To learn more about the derived formula, continue reading!
Think about cutting a pizza into 3 slices. what would a slice's area be? One-third! Mathematically, we would find the entire area of the pizza pie before multiplying by one-third (or dividing by 3). If a pie has been split evenly into 3 that means the pie's 360 degree angle has been split evenly, (each slice has the same central angle value) or into 360/3 = 120 degrees! Note that 120 is one-third of 360.
The ratio of the slice's central angle to 360 degrees is proportional to the ratio of the area of the slice to the pie.
This idea is exemplified in the formula, how much of the angle is going to be sliced off relative to the circle/pie: [tex](\frac{x}{360} )[/tex]; okay now that's how much of the entire pie's area, [tex]r^2\pi[/tex], the slice is going to have.
Go here to learn more about central angles:
https://brainly.com/question/34806899?referrer=searchResults
