Question

Is my solution correct?​

Answer 1

Answer:

The area of the shaded sector is $51.2\pi \ units^{2}$

Step-by-step 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

$\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}$