Finding Perimeter/Circumference of part of a circle

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To find the perimeter and area of the shaded region between two circles with inner radius 2.9 m and outer radius 6.5 m, and an angle of 110 degrees, the correct approach involves using the formula for circumference and area of an annulus. The total circumference for each radius is calculated using C=2πr, and the arc length is found by multiplying this circumference by the ratio of the angle to 360 degrees. The area of the shaded region is determined by subtracting the area of the inner circle from the area of the outer circle, calculated as π(R^2 - r^2). The expected answers for the perimeter and area are 25.3 m and 32.5 m², respectively. Understanding how the angle affects the calculations is crucial for solving the problem accurately.
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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
 
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sdoyle1 said:

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.
 
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
 
Last edited by a moderator:
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?
 
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.
 
The problem doesn't include a picture?
 

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