Mathematics Question and Solution
Calculating R, radius of the quarter circle.
¼πR²=64π²
R = 16√(π) cm
Calculating x, radius of the green inscribed semi circle.
(2x)²+x²=(16√(π))²
Therefore;
5x² = 256π
x = (16√(5π))/5 cm
It implies;
Area green inscribed semi circle is;
½π((16√(5π))/5)²
= (256π²)/10 cm²
Calculating y, radius of the blue inscribed semi circle.
(2y)²+(y+x)²=(16√(π))²
Therefore;
4y²+y²+(32√(5π)y)/5+(256π)/5=256π
25y²+32√(5π)y-1024π= 0
y = √(25856π/625)- √(256*5π/625)
y = 8.86375260683 cm
Area blue inscribed semi circle is;
½π(8.86375260683)²
= 123.411357431 cm²
Calculating z, radius of the yellow inscribed semi circle.
(2z)²+(z+y+x)²=(16√(π))²
Therefore;
4z²+(z+21.5463999592)²=(16√(π))²
5z²+43.0927999184z-340.000368117=0
It implies;
z = 4.99502 cm
Area yellow inscribed semi circle is;
½π(4.99502)²
= 39.1917214692 cm²
