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The measure of central angle XYZ is 3 pie / 4 radians.
What is the area of the shaded sector?
35 pie units square
85 pie units square
96 pie units square
256 pie units square

The measure of central angle XYZ is 3 pie 4 radians What is the area of the shaded sector 35 pie units square 85 pie units square 96 pie units square 256 pie un class=

Respuesta :

JeanaShupp

Answer: [tex]96\pi\text{ units}^2[/tex]

Step-by-step explanation:

From the given picture, it can be seen that the radius of the circle = 16 units

Also, the measure of central angle XYZ [tex]=\dfrac{3}{4}\pi[/tex] radians

The area of sector with radius r and angle x radian is given by :-

[tex]\text{Area of sector}=\dfrac{1}{2}r^2\ x[/tex]

Now, the area of the shaded sector is given by :-

[tex]\text{Area of the shaded sector}=\dfrac{1}{2}(16)^2\dfrac{3}{4}\pi\\\\\Rightarrow\text{Area of the shaded sector}=96\pi\text{ units^2}[/tex]

Answer:

Option C. 96 pie units square

Step-by-step explanation:

We have to find the area of shaded sector of the circle.

Area of a sector formed by an arc = [tex]\frac{RL}{2}[/tex]

Where R = Radius of the circle

and L = Length of the arc.

for area of the sector we will find the length of arc first.

Since [tex]L=R\theta[/tex] when L is length of arc.

by putting [tex]\theta[/tex] = [tex]\frac{3\pi }{4}[/tex]×16 = ( [tex]3\pi[/tex] ) (4)

= [tex]12\pi[/tex] unit

Area of the shaded sector = [tex]\frac{RL}{2}[/tex]

[tex]A=\frac{(16)*(12\pi)}{2}[/tex]

= 8 ×[tex]12\pi[/tex] = [tex]96\pi unit^{2}[/tex]

Option C. 96 pie units square