The measure of central angle xyz is radians. what is the area of the shaded sector? 32 85 96 256

Asked by maham237 @ 27/12/2020 in Mathematics viewed by 322 People

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

Answered by maham237 @ 27/12/2020

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 :-

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

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