Mathematics Question and Solution
a = 6+4
a = 10 cm.
b²+6² = 10²
b = √(100-36)
b = √(64)
b = 8 cm.
c = b+4
c = 12 cm.
d = c-r
d = (12-r) cm.
r is the ascribed half circle radius.
e = 6+d
e = 6+(12-r)
e = (18-r) cm.
Calculating r, radius of the ascribed half circle.
r² = (18-r)²+6²
r² = 324-36r+r²+36
36r = 360
r = 10 cm.
Area Painted is
Area half circle with radius 10 cm - Area half circle with radius 6 cm - Area half circle with radius 4 cm.
= ½*π*10²-½*π*6²-½*π*4²
= ½(100π-36π-16π)
= ½(100π-52π)
= ½(48π)
= 24π cm²
