In the circle illustrated, the circumference...

Question 1 of 270705eccef9dbacbc34ba4d45dec

In the circle illustrated, the circumference is 75.36 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 75.36 inches. What is the area of the shaded portion? See illustration GS-0134.

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🔍 Key Concepts

• Use the circle’s circumference (75.36 in) and the formula $C = 2\pi R$ to find the radius R of the circle. • Recognize that the shaded region is a sector of the circle minus a right triangle formed by two radii. • Use formulas for area of a sector and area of a right triangle to express the shaded area.

💭 Think About

• Once you find the radius, what fraction of the full circle does the shaded sector represent, based on the central angle shown in the illustration? • How can you write an expression for the area of the sector, and then subtract the area of the right triangle with legs equal to the radius? • After you compute the shaded area, which answer choice is closest to your result when using $\pi \approx 3.14$ ?

✅ Before You Answer

• First, compute radius R carefully from $C = 75.36 \text{ in} = 2\pi R$ . • Confirm that the central angle between the two radii forming the triangle is 90°, making it a quarter-circle sector and a right isosceles triangle (legs = R). • Check units: all lengths in inches, all results in square inches, and keep enough decimal places when multiplying and subtracting.