Determine the shaded area. The radius of the circle is 9 inches. The length of the rectangle is 21 inches

Accepted Solution

Answer:The area of shaded region is 123.66 [tex]in^2[/tex].Step-by-step explanation:Given:Below is the figure shown in which a circle with radius 9 inches is placed in a rectangle with length is 21 inches and we need to find the area of shaded region or leftover region.Now we will first find the area of circle whose radius r = 9 inches.Hence, Area of circle = [tex]\pi r^2= 3.14\times 9 \times9= 254.34\ in^2[/tex]Now we will find Area of rectangle whose length is 21 inches and width will be equal to diameter of the circle.diameter of circle = 2 [tex]\times[/tex] radius = [tex]2\times 9= 18 \ in[/tex]hence width of rectangle = diameter of circle = 18 in.Area of rectangle = length [tex]\times[/tex] width =[tex]21 \times 18 =378 \ in^2[/tex]Area of Shaded region = Area of rectangle - Area of circle = [tex]378 \ in^2 - 254.34\ in^2 = 123.66 \ in^2[/tex]