To solve this, we are going to use the formula for the area of the sector of a circle:

where

is the area of the circular sector.

is the radius of the circle.

is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so . We can also infer from the picture that the radius of the circle is 3in, so . Lets replace those values in our formula to find :

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula:

where

is the arc length.

us the radius of the circle.

is the central angle.

We know from our problem that , and , so lets replace those values in our formula:

We can conclude that the length of the arc is indeed 3 inches.

where

is the area of the circular sector.

is the radius of the circle.

is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so . We can also infer from the picture that the radius of the circle is 3in, so . Lets replace those values in our formula to find :

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula:

where

is the arc length.

us the radius of the circle.

is the central angle.

We know from our problem that , and , so lets replace those values in our formula:

We can conclude that the length of the arc is indeed 3 inches.

where

is the area of the circular sector.

is the radius of the circle.

is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so . We can also infer from the picture that the radius of the circle is 3in, so . Lets replace those values in our formula to find :

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula:

where

is the arc length.

us the radius of the circle.

is the central angle.

We know from our problem that , and , so lets replace those values in our formula:

We can conclude that the length of the arc is indeed 3 inches.

False

Step-by-step explanation:

Radius of circle = r = 2.5 in

Length of arc of the circle = s = 2 in

Central angle in radians = θ

The length of arc of the circle is the product of the radius and the central angle in radians.

s = rθ

θ = 0.8 radians

The measure of angle θ is not 1 radian but 0.8 radian.

False

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