🔍 Key Concepts

• Use the circle’s circumference to find the radius using ( C = 2\pi R ) • Recognize that the shaded region is part of a sector of a circle minus a right triangle • Use the area formulas: (A_{\text{circle}} = \pi R^2), (A_{\text{sector}} = \frac{\theta}{360^\circ}\pi R^2), and (A_{\text{triangle}} = \tfrac{1}{2}ab)

💭 Think About

• What is the radius of the circle if the circumference is 125.6 inches and you use (\pi \approx 3.14)? • What central angle (in degrees) is formed between the two radii that make the sides of the right triangle? How does that relate to the sector area? • Once you have the sector area and the triangle area, how can you combine them to get just the shaded part?

✅ Before You Answer

• Confirm you solved for R correctly from (125.6 = 2\pi R) • Make sure the right triangle’s legs are both equal to R, and you are using (A = \tfrac{1}{2}R^2) for its area • After subtracting, compare your final shaded area with the choices and check which value is closest to your result