Finding components of a circle.

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I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem.



The following diagram shows a circle with centre o and radius 5 cm.
picture of circle
The points A, B, and C like on the circumference of the circle, and $angle AOC$ = 0.7 radians.

a. Find the length of the arc ABC.

b. Find the perimeter of the shaded sector.

c. Find the area of the shaded sector.



For a, the arc length would be the angle multiplied by the radius, correct?



l = 5 x 0.7
l = 3.5 cm



For b, would it be 2 radii and the length of the arc added together?

5+5+3.5 = 13.5 cm



And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$




circle




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  • We can use the fact that the area is proportional to the angle.
    – gimusi
    Aug 6 at 20:14














up vote
3
down vote

favorite












I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem.



The following diagram shows a circle with centre o and radius 5 cm.
picture of circle
The points A, B, and C like on the circumference of the circle, and $angle AOC$ = 0.7 radians.

a. Find the length of the arc ABC.

b. Find the perimeter of the shaded sector.

c. Find the area of the shaded sector.



For a, the arc length would be the angle multiplied by the radius, correct?



l = 5 x 0.7
l = 3.5 cm



For b, would it be 2 radii and the length of the arc added together?

5+5+3.5 = 13.5 cm



And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$




circle




share|cite|improve this question





















  • We can use the fact that the area is proportional to the angle.
    – gimusi
    Aug 6 at 20:14












up vote
3
down vote

favorite









up vote
3
down vote

favorite











I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem.



The following diagram shows a circle with centre o and radius 5 cm.
picture of circle
The points A, B, and C like on the circumference of the circle, and $angle AOC$ = 0.7 radians.

a. Find the length of the arc ABC.

b. Find the perimeter of the shaded sector.

c. Find the area of the shaded sector.



For a, the arc length would be the angle multiplied by the radius, correct?



l = 5 x 0.7
l = 3.5 cm



For b, would it be 2 radii and the length of the arc added together?

5+5+3.5 = 13.5 cm



And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$




circle




share|cite|improve this question













I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem.



The following diagram shows a circle with centre o and radius 5 cm.
picture of circle
The points A, B, and C like on the circumference of the circle, and $angle AOC$ = 0.7 radians.

a. Find the length of the arc ABC.

b. Find the perimeter of the shaded sector.

c. Find the area of the shaded sector.



For a, the arc length would be the angle multiplied by the radius, correct?



l = 5 x 0.7
l = 3.5 cm



For b, would it be 2 radii and the length of the arc added together?

5+5+3.5 = 13.5 cm



And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$





circle





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 6 at 20:15
























asked Aug 6 at 20:04









Ella

999




999











  • We can use the fact that the area is proportional to the angle.
    – gimusi
    Aug 6 at 20:14
















  • We can use the fact that the area is proportional to the angle.
    – gimusi
    Aug 6 at 20:14















We can use the fact that the area is proportional to the angle.
– gimusi
Aug 6 at 20:14




We can use the fact that the area is proportional to the angle.
– gimusi
Aug 6 at 20:14










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










For point $a$ and $b$ your answers are correct.



For the area we have that for the whole circle



  • $A(2pi)=pi r^2=frac12 cdot 2picdot r^2$

therefore for an angle $theta$ since the area is proportional to the angle



  • $A(theta)=frac12 theta r^2$

with $theta$ expressed in radians.






share|cite|improve this answer

















  • 1




    Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
    – Ella
    Aug 6 at 20:19






  • 1




    @Ella Yes exactly that's correct!
    – gimusi
    Aug 6 at 20:21










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










For point $a$ and $b$ your answers are correct.



For the area we have that for the whole circle



  • $A(2pi)=pi r^2=frac12 cdot 2picdot r^2$

therefore for an angle $theta$ since the area is proportional to the angle



  • $A(theta)=frac12 theta r^2$

with $theta$ expressed in radians.






share|cite|improve this answer

















  • 1




    Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
    – Ella
    Aug 6 at 20:19






  • 1




    @Ella Yes exactly that's correct!
    – gimusi
    Aug 6 at 20:21














up vote
1
down vote



accepted










For point $a$ and $b$ your answers are correct.



For the area we have that for the whole circle



  • $A(2pi)=pi r^2=frac12 cdot 2picdot r^2$

therefore for an angle $theta$ since the area is proportional to the angle



  • $A(theta)=frac12 theta r^2$

with $theta$ expressed in radians.






share|cite|improve this answer

















  • 1




    Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
    – Ella
    Aug 6 at 20:19






  • 1




    @Ella Yes exactly that's correct!
    – gimusi
    Aug 6 at 20:21












up vote
1
down vote



accepted







up vote
1
down vote



accepted






For point $a$ and $b$ your answers are correct.



For the area we have that for the whole circle



  • $A(2pi)=pi r^2=frac12 cdot 2picdot r^2$

therefore for an angle $theta$ since the area is proportional to the angle



  • $A(theta)=frac12 theta r^2$

with $theta$ expressed in radians.






share|cite|improve this answer













For point $a$ and $b$ your answers are correct.



For the area we have that for the whole circle



  • $A(2pi)=pi r^2=frac12 cdot 2picdot r^2$

therefore for an angle $theta$ since the area is proportional to the angle



  • $A(theta)=frac12 theta r^2$

with $theta$ expressed in radians.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 6 at 20:10









gimusi

65.5k73684




65.5k73684







  • 1




    Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
    – Ella
    Aug 6 at 20:19






  • 1




    @Ella Yes exactly that's correct!
    – gimusi
    Aug 6 at 20:21












  • 1




    Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
    – Ella
    Aug 6 at 20:19






  • 1




    @Ella Yes exactly that's correct!
    – gimusi
    Aug 6 at 20:21







1




1




Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
– Ella
Aug 6 at 20:19




Using this formula, I entered A = 1/2 x 0.7 x $5^2$ and got 8.75$cm^2$ as my answer. Does this sound right?
– Ella
Aug 6 at 20:19




1




1




@Ella Yes exactly that's correct!
– gimusi
Aug 6 at 20:21




@Ella Yes exactly that's correct!
– gimusi
Aug 6 at 20:21












 

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