Mathematics Question and Solution
Calculating Area Red.
Let x be the radius of the smallest inscribed white half circle.
a = 2x units.
a is the radius of the smaller inscribed white circle and also the radius of the red and smallest white circle.
c = 3x units.
c is the radius of the red and smaller white circle.
Calculating x.
4²+x² = (3x)²
16+x² = 9x²
8x² = 16
x = √(2) units.
Recall.
a = 2x
And x = √(2) units.
a = 2√(2) units.
Again, a is the radius of the smaller inscribed white circle and also the radius of the red and smallest white circle.
c = 3x units.
And x = 2√(2) units.
c = 3√(2) units
Again, c is the radius of the red and smaller white circle.
Therefore, red area is;
Area half circle with radius 3√(2) units + Area half circle with radius 2√(2) units - Area half circle with radius 2√(2) units - Area half circle with radius √(2) units.
½(3√(2))²π+½(2√(2))²π-½(2√(2))²π-½√(2)²π
= ½(3√(2))²π-½√(2)²π
= ½(18π)-½(2π)
= ½(16π)
= 8π square units.
