Mathematics Question and Solution
a = ⅐(360)°
a is the interior angle of each of the congruent 7 sectors.
Let the radius of the ascribed circle be 1 unit.
Area ascribed circle is;
π(1²)
= π square units.
c = (1-b) units.
b is the radius of each of the 7 congruent inscribed half circles.
Calculating b.
sin(⅐(360)) = b/(1-b)
0.7818314825 = b/(1-b)
0.7818314825-0.7818314825b = b
1.7818314825b = 0.7818314825
b = 0.7818314825/1.7818314825
b = 0.4387796995 units.
Again, b is the radius of each of the 7 congruent inscribed half circles.
Area 7 congruent inscribed half circles is;
7*½(πb²)
= 7*½(0.4387796995²)π
= 0.6738466864π square units.
Therefore, shaded fraction is;
Area 7 congruent inscribed half circles ÷ Area ascribed circle.
= 0.6738466864π÷π
= 0.6738466864
