Finding Perimeter/Circumference of part of a circle

[sdoyle1]

Homework Statement

The inner radius is measured from a point A and is 2.9 m. The outer radius is measured from the same point A and is 6.5 m. The angle at A is 110*. What is the Perimeter of the shaded area in meters? What is the area of the shaded are in square meters?

Homework Equations

C=2rpi

The Attempt at a Solution

Just for part A I tried to find the total circumference as if the circle was a full 360* and then multiplied the resulting answer by the ratio of 110*/360*. The answer was incorrect. The answers are suppose to be 25.3 m and 32.5 m^2

 

[Mark44]

Homework Statement

The inner radius is measured from a point A and is 2.9 m. The outer radius is measured from the same point A and is 6.5 m. The angle at A is 110*. What is the Perimeter of the shaded area in meters? What is the area of the shaded are in square meters?

Homework Equations

C=2rpi

The Attempt at a Solution

Just for part A I tried to find the total circumference as if the circle was a full 360* and then multiplied the resulting answer by the ratio of 110*/360*. The answer was incorrect. The answers are suppose to be 25.3 m and 32.5 m^2

From your description, it seems that you need to find the perimeter and area of a section of a ring or annulus.

The circumference of a circle is C = r * 2pi. The arc length along the portion of a circle subtended by an arc whose measure is theta (in radians) is r * theta.

The area of an annulus is pi(R^2 - r^2), where R and r represent the outer and inner radii respectively.

 

[ammontgo]

We know the area of a circle as:
[PLAIN]https://dl.dropbox.com/u/4645835/MATH/Area%20of%20Circle.gif

Part B:
We want to find the area of the shaded portion. So, we find the area of the outside circle and subtract from it the area of the inside circle.

[PLAIN]https://dl.dropbox.com/u/4645835/MATH/Worked.gif

 

[Mark44]

Well, I don't know what the drawing looks like, so I don't know exactly what the problem is. How does the angle of 110 degrees enter into the problem?

 

[ammontgo]

I imagine it as a larger circle around a smaller circle. The shaded region they are referring to would be the area enclosed by the two circles. The given angle...according to my interpretation...is between the 0 degree line and the radii extending from point A.

 

[Mark44]

The problem doesn't include a picture?