+0  
 
0
61
2
avatar

What is the ratio of the Blue area to the Yellow area to the Red area?  (A quarter-circle is constructed. A semi-circle is constructed on the radius of the quarter circle. Finally, a circle of maximum radius is inscribed in the semi-circle)

 

 Jan 12, 2020
 #1
avatar+20254 
+1

Orange area is 1/4 pi r^2      (well, the WHOLE quadrant is)

yellow area is 1/2 pi (1/2 r)^2   ( this is the semicircle area....blue will be subtracted shortly)

blue area is     pi (1/4r)^2

 

Divide all be pi

 

Blue area       :     yellow semi-circle - blue circle     :       red quarter  - yellow   semicircle

 

1/16 r^2  : 1/8 r^2 - 1/16r^2 : 1/4 r^2 -1/8r^2                 Divide out the r^2    and simplify

 

1/16   :  1/16  :  1/8  

1/16  : 1/16 : 1/8

1:1:2                                             

 

      CORRECTED !   THANX to Dragan who noticed my error.....I originally listed the red as an entire quarter and the yellow as a full semicircle !

 Jan 12, 2020
edited by ElectricPavlov  Jan 26, 2020
 #2
avatar+370 
+1

I think that your answer is not correct. Read the question carefully.

 

The correct answer is:   

   The ratio of the Blue area to the Yellow area to the Red area is:      1 : 1 : 2    indecision

Dragan  Jan 20, 2020

8 Online Users