Question

Is my solution correct?​

Answer 1

The area of the shaded sector is
`51.2\pi \ units^(2)`

Explanation:

I assume that the problem is

Find the area of the shaded sector of the circle with radius equal to 16 units

step 1

Find the value of x

we know that

`8x+2x=360\°`-----> by complete circle

`10x=360\°`

`x=36\°`

The central angle of the shaded sector is 2x

`2(36\°)=72\°`

step 2

Find the area of the circle

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=16\ units`

substitute

`A=\pi (16)^(2)`

`A=256\pi\ units^(2)`

step 3

Find the area of the shaded sector

we know that

A central angle of 360 degrees subtends an area of circle equal to
`256\pi\ units^(2)`

so

by proportion

Find the area of the shaded sector by a central angle of 72 degrees

`(256\pi)/(360)=(x)/(72) \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^(2)`