Question

The measure of central angle XYZ is 3 pie / 4 radians.

Answer 1

Answer: $96\pi\text{ units}^2$

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 $=\dfrac{3}{4}\pi$ radians

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

$\text{Area of sector}=\dfrac{1}{2}r^2\ x$

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

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

Answer 2

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 = $\frac{RL}{2}$

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 $L=R\theta$ when L is length of arc.

by putting $\theta$ = $\frac{3\pi }{4}$×16 = ( $3\pi$ ) (4)

= $12\pi$ unit

Area of the shaded sector = $\frac{RL}{2}$

$A=\frac{(16)*(12\pi)}{2}$

= 8 ×$12\pi$ = $96\pi unit^{2}$

Option C. 96 pie units square