Question

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

Answer 1

Option C. 96 pie units square

Explanation:

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

Area of a sector formed by an arc =
`(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` =
`(3\pi )/(4)`×16 = (
`3\pi` ) (4)

=
`12\pi` unit

Area of the shaded sector =
`(RL)/(2)`

`A=((16)*(12\pi))/(2)`

= 8 ×
`12\pi` =
`96\pi unit^(2)`

Option C. 96 pie units square

Answer 2

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

Explanation:

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

Also, the measure of central angle XYZ
`=(3)/(4)\pi` radians

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

`\text{Area of sector}=(1)/(2)r^2\ x`

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

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