Answer:
96π units²
Step-by-step explanation:
area of shaded sector (A) = area of circle × fraction of circle
A = πr² × [tex]\frac{\frac{3\pi }{4} }{2\pi }[/tex]
= 16² × [tex]\frac{3\pi }{8}[/tex]
= 256 × [tex]\frac{3\pi }{8}[/tex]
= 32 × 3π
= 96π units²
Answer:
Area of sector : 96 π unit².
Step-by-step explanation:
Given : The measure of central angle XYZ is 3pi/4 radians.
To find : What is the area of the shaded sector?
Solution: We have given central angle XYZ is 3pi/4 radians.
Area of sector : [tex]\frac{1}{2}[/tex] (radius)²* central angle.
Plug the values central angle = [tex]\frac{3\pi }{4}[/tex] , radius = 16 units.
Then ,
Area of sector : [tex]\frac{1}{2}[/tex] (16)²* [tex]\frac{3\pi }{4}[/tex].
Area of sector : [tex]\frac{1}{2}[/tex] * 256 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 128 * [tex]\frac{3\pi }{4}[/tex].
Area of sector : 32 * 3 π
Area of sector : 96 π unit².
Therefore, Area of sector : 96 π unit².
