又去AI喵了一眼，AI居然说阴影面积是0

还头头是道 

 

Solution for the shaded area: 

 

1. 1. Identify the shapes:

   The image shows a quarter circle with a circular hole cut out of it. The dimension '12' represents the diameter of the circular hole, which is also equal to the radius of the quarter circle.
2. 2. Determine the radius of the circle and quarter circle:

   The diameter of the circular hole is 12, so its radius is

   

   rhole=12/2=6r sub h o l e end-sub equals 12 / 2 equals 6

   ?????????????????=12/2=6

   . The radius of the quarter circle is

   

   Rqc=12cap R sub q c end-sub equals 12

   ????????????=12

   .
3. 3. Calculate the area of the quarter circle:

   The area of a full circle is

   

   πR2pi cap R squared

   ????????2

   , so the area of a quarter circle is

   

   14πR2one-fourth pi cap R squared

   14????????2

   . 

    

Area of quarter circle =

14π(12)2=14π(144)=36πone-fourth pi open paren 12 close paren squared equals one-fourth pi open paren 144 close paren equals 36 pi

14????(12)2=14????(144)=36????

. 

 

1. 4. Calculate the area of the circular hole:

   The area of a circle is

   

   πr2pi r squared

   ????????2

   .

 

Area of circular hole =

π(6)2=36πpi open paren 6 close paren squared equals 36 pi

????(6)2=36????

. 

 

1. 5. Calculate the total shaded area:

   The shaded area is the area of the quarter circle minus the area of the circular hole.

 

Total shaded area = Area of quarter circle - Area of circular hole =

36π−36π=036 pi minus 36 pi equals 0

36????−36????=0

.