In the circle illustrated, the circumference...

Question 1 of 270705eccef9dbacbc34ba4d45de6

In the circle illustrated, the circumference is 62.8 feet. What is the area of the shaded portion? See illustration GS-0134.

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Question 1 of 27070

Q

In the circle illustrated, the circumference is 62.8 feet. What is the area of the shaded portion? See illustration GS-0134.

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🔍 Key Concepts

• Use the circle formula for circumference to find the radius:
$C = 2\pi r$ • Recognize what fraction of the full circle the shaded region comes from (look at the right angle between the two radii). • The shaded area is the difference between a circular sector and a right triangle.

💭 Think About

• From the given circumference, what is the radius of the circle in feet? • What is the area of the sector formed by the two radii that meet at the right angle? • What is the area of the right triangle whose legs are along those two radii, and how does that relate to the shaded region?

✅ Before You Answer

• Be sure to use $C = 2\pi r$ with consistent units (feet). • Confirm the central angle between the two radii forming the triangle by using the right-angle mark in the figure. • Compute: shaded area = sector area − triangle area, not the other way around.