A scientist enlarged a circular portion of a microscope slide to make it easier to count the number of bacteria present in the sample.He divided the circle into 5 sectors as shown below and plans to count bacteria only in the shaded sector. What is the area of the shaded sector to the nearest tenth of a square centimeter A.141.4B.212.1C.377.0D.424.1

Answer:Option B. [tex]212.1\ cm^{2}[/tex]Step-by-step explanation:step 1Find the central angle of the shaded sectorRemember that the diameter divide the circle into two equal parts ( 180 degrees each part)soLetx -----> the measure of the central angle of the shaded sector∠x+72°=180°∠x=180°-72°=108°step 2Find the area of the circleThe area of the circle is [tex]A=\pi r^{2}[/tex]we have[tex]r=15\ cm[/tex]assume[tex]\pi=3.1416[/tex]substitute[tex]A=(3.1416)(15)^{2}[/tex][tex]A=706.86\ cm^{2}[/tex]step 3Find the area of the shaded sectorRemember that the area of the complete circle subtends a central angle of 360 degreessoby proportion find the area of a sector by a central angle of 108 degrees[tex]\frac{706.86}{360}=\frac{x}{108}\\ \\x=706.86*108/360\\ \\x=212.1\ cm^{2}[/tex]