Question

The measure of central angle XYZ is 3pi/4 radians. What is the area of the shaded sector?

32pi units2
85 ..
96 ..
256 ..

Answer 1

96π units²

Explanation:

area of shaded sector (A) = area of circle × fraction of circle

A = πr² ×
`((3\pi )/(4) )/(2\pi )`

= 16² ×
`(3\pi )/(8)`

= 256 ×
`(3\pi )/(8)`

= 32 × 3π

= 96π units²

Answer 2

Area of sector : 96 π unit².

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 :
`(1)/(2)` (radius)²* central angle.

Plug the values central angle =
`(3\pi )/(4)` , radius = 16 units.

Then ,

Area of sector :
`(1)/(2)` (16)²*
`(3\pi )/(4)`.

Area of sector :
`(1)/(2)` * 256 *
`(3\pi )/(4)`.

Area of sector : 128 *
`(3\pi )/(4)`.

Area of sector : 32 * 3 π

Area of sector : 96 π unit².

Therefore, Area of sector : 96 π unit².