Mathematics Question and Solution
Notice!
Radius of the ascribed semi circle is 6 cm.
It implies;
Radius, a of the inscribed bigger circle is;
a = ½(6)
a = 3 cm.
Calculating b, radius of the smaller inscribed circle.
c = (6-b) cm.
c² = b²+e²
(6-b)² = b²+e²
e² = 36-12b
e = √(36-12b) cm.
f = (3-b) cm.
g = (3+b) cm.
Therefore;
g² = f²+e²
(3+b)² = (3-b)²+36-12b
9+6b+b² = 9-6b+b²+36-12b
12b = 36-12b
24b = 36
b = (36/24)
b = (3/2) cm.
Again, b is the radius of the smaller inscribed circle.
Painted Area is;
Area semi circle with radius 6 cm - Area circle with radius 3 cm - Area circle with radius (3/2) cm.
= ½*6*6π-3*3π-(3/2)(3/2)π
= 18π-9π-(9/4)π
= 9π-(9/4)π
= ¼(27π) cm²
