Answer:
Step-by-step explanation:
Problem 65:
We can find the area of the shaded regions by finding the total area of the circle and then multiplying it by the angle/360.
The radius is 11 inches, so plugging that in, we get that:
Area = 121[tex]\pi[/tex] x (53+72)/360 = 121[tex]\pi[/tex] x 125/360 = around 42.01388[tex]\pi[/tex] inches squared or around 131.99 inches squared when put in a calculator.
Problem 66:
First, we find the area of the shaded region inside the smaller circle, then find the area of the region in the larger circle combined with the smaller cut part, then remove that area.
The radius of the smaller circle is 8cm, so the area is:
Area = 64[tex]\pi[/tex] x 88/360 = around 15.6444[tex]\pi[/tex] centimeters squared or around 49.15 centimeters squared when put in a calculator.
Now, we find the area of the larger shaded region:
Area = (400[tex]\pi[/tex] x 104/360) - (64[tex]\pi[/tex] x 104/360)
Simplifying, we get:
343.92 - 58.08 = 285.84 centimeters squared.
Adding 285.84 to 49.15, we get the total area = 334.89 centimeters squared.
Solution: 65: 131.99[tex]in^{2}[/tex] and 66: 334.89[tex]cm^{2}[/tex]
