In the circle illustrated, the circumference...

Question 1 of 270705eccef9dbacbc34ba4d45ded

In the circle illustrated, the circumference is 125.6 inches. What is the area of the shaded portion? See illustration GS-0134.

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Question 1 of 27070

In the circle illustrated, the circumference is 125.6 inches. What is the area of the shaded portion? See illustration GS-0134.

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🔍 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