In the circle illustrated, the circumference...

Question 1 / 205eccef9dbacbc34ba4d45ded

Question 1 of 205eccef9dbacbc34ba4d45ded

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 20

5eccef9dbacbc34ba4d45ded

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

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Question 1 of 20

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

234.0 square inches

107.0 square inches

114.1 square inches

214.0 square inches

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Question 1 / 205eccef9dbacbc34ba4d45ded

Question 1 of 205eccef9dbacbc34ba4d45ded

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

Back

Question 1 of 20

5eccef9dbacbc34ba4d45ded

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

No comments yet

Be the first to share your thoughts!

If the question has a related picture, it will appear here.

🔍 Key Concepts

💭 Think About

✅ Before You Answer

👋 Hi! I'm Genie, your AI study assistant. How can I help you with this question?

Quick actions

— No credit card needed