MATH SOLVE

5 months ago

Q:
# Is my solution correct?

Accepted Solution

A:

Answer:The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]Step-by-step explanation:I assume that the problem isFind the area of the shaded sector of the circle with radius equal to 16 unitsstep 1Find the value of xwe know that[tex]8x+2x=360\°[/tex]-----> by complete circle[tex]10x=360\°[/tex][tex]x=36\°[/tex]The central angle of the shaded sector is 2x[tex]2(36\°)=72\°[/tex]step 2Find the area of the circleThe area of the circle is equal to[tex]A=\pi r^{2}[/tex]we have[tex]r=16\ units[/tex]substitute[tex]A=\pi (16)^{2}[/tex][tex]A=256\pi\ units^{2}[/tex]step 3Find the area of the shaded sectorwe know thatA central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]so by proportionFind the area of the shaded sector by a central angle of 72 degrees[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]