Lesson OVERVIEW of LESSONS on Area of a Circle, a Sector and a Segment of the circle

Algebra ->  Surface-area -> Lesson OVERVIEW of LESSONS on Area of a Circle, a Sector and a Segment of the circle      Log On


   

This Lesson (OVERVIEW of LESSONS on Area of a Circle, a Sector and a Segment of the circle) was created by by ikleyn(52832) About Me : View Source, Show
About ikleyn:

OVERVIEW of LESSONS on Area of a Circle, a Sector and a Segment of the circle

For your convenience,  this file contains
     - the list of my lessons on area of a circle,  area of a sector and area of a segment of the circle in this site,
     - the major formulas for calculating the area of a circle,  area of a sector and area of a segment of the circle,  and
     - the list of relevant solved problems.

The major formulas for calculating the area of a circle, area of a sector and area of a segment of the circle

    - The area of a  circle  equals  pi%2Ar%5E2,  where  r  is the radius of the circle and  pi  is the ratio of the circle circumference to its diameter,  pi = 3.14 . . . .

    - The area  S  of a  sector  of the circle with the radius  r  and the central angle of the radian measure  alpha  is equal                

          S = 1%2F2alpha%2Ar%5E2.


    - The area  S  of a  segment of the circle  with the radius  r  and the central angle of the radian measure  alpha  is equal           

          S = 1%2F2[alpha+-+sin%28alpha%29].r%5E2.



The list of my lessons on area of a circle, area of a sector and area of a segment of the circle

    - Area of a circle,
    - Area of a sector  and
    - Area of a segment of the circle
under the current topic  Area and surface area  of the section  Geometry,  and
    - Solved problems on area of a circle,
    - Solved problems on area of a sector,
    - Solved problems on area of a segment of the circle  and
    - Solved problems on area of a circle, a sector and a segment of the circle
under the topic  Geometry  of the section  Word problems.


The list of solved problems on area of a circle, area of a sector and area of a segment of the circle

Lessons  Area of a circle  and  Solved problems on area of a circle

     - Find the area of a circle which has the radius of  10 cm.
     - Find the area of a ring concluded between two concentric circles that have the radii of  10 cm  and  6 cm.          
     - Find the area of the circle which is inscribed in the  60°-sector of the circle with the radius of  12 cm.
     - Find the area of the circle which is inscribed in the  90°-sector of the circle with the radius of  10 cm.
     - Find the area of a semicircle inscribed in a triangle with the side measures of  13 cm,  14 cm  and  15 cm
          in a way that the center and the diameter of the semicircle lie on the side of the measure  14 cm  of
          the triangle.





     


     

Lessons  Area of a sector  and  Solved problems on area of a sector

     - Find the area of a  72°-sector of the circle which has the radius of  10 cm.
     - Find the area of the figure which is restricted by the contour of a square with the side of  10 cm  from            
          the bottom and from the lateral sides and by a semicircle from the top.
     - Find the area of the figure which is obtained from a square with the side of  10 cm  after cutting off
          a semicircle of the radius of  6 cm.

     

     - Find the area of a figure comprised of a circle and an angle between two tangent lines released from a
          point outside the circle,  if the circle radius is of  10 cm and the angle between the tangent lines is of  60°.    
     - Find the area of a figure restricted by a circle and by two tangent lines released from a point outside
          the circle,  if the circle radius is of  10 cm and the angle between the tangent lines is of  60°.
          The interior of the circle is not included to the figure.
     - Find the area of a figure restricted by three congruent circles that touch each the other,  if the circles
          radius is of  r = 10 cm.




    


    


Lessons  Area of a segment of the circle  and  Solved problems on area of a segment of the circle

     - Find the area of a  72°-segment of the circle which has the radius of  10 cm.
     - Find the area of a figure restricted by two circles that have equal radii of 10 cm,  if the distance between          
          their centers is of  10 cm  also.
     - Find the area of a figure restricted by two circles with the centers at the opposite vertices of a square
          and the radii equal to the square side  a = 10 cm.



     

Lesson  Solved problems on area of a circle, a sector and a segment of the circle

     - Find the area of the intersection of two circles on a plane,  if the circles have the same radius of
          r = 10 cm  and the intersection segments have the central angle  alpha  of  a) 60°;  b) 90°;  c) 120°.

     - Find the area covered by the union of two intersecting circles on a plane,  if the circles have the
          same radius of  r = 10 cm  and the intersection segments have the central angle  alpha  of
          a) 60°;  b) 90°;  c) 120°.
     - Find the area of a  lune  shape formed by two intersecting circles on a plane,  if the circles have
          the same radius of  r = 10 cm  and the intersection segment have the central angle  alpha  of
          a) 60°;  b) 90°;  c) 120°.

  





  





  


To navigate over all topics/lessons of the Online Geometry Textbook use this file/link  GEOMETRY - YOUR ONLINE TEXTBOOK.

This lesson has been accessed 2558 times.