Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
(a) Exact radius of the circle is;
½√(2²+4²)
= ½√(20)
= ½*2√(5) units.
= √(5) units.
Or
Cos(atan(2)) = (1/r)
Where r is the radius of the circle.
r = 1/cos(atan(2)))
r = √(5) units.
(b) Area Yellow exactly is;
Area triangle with height 2 units and base 2sin(2atan2) units + Area triangle with height ⅕(8√(5)) units and base 8sin(90-asin(√(5)/5)) units - Area triangle with height ⅓(16) units and base 2√(5)sin(asin(√(5)/5)) units.
= ½*2*2sin(2atan(2)) + ½*⅕(8√(5))*8sin(90-asin(√(5)/5)) - ½*⅓(16)*2√(5)sin(asin(√(5)/5))
= ⅕(8) + ⅕(64) - ⅓(16)
= ⅕(72) - ⅓(16)
= 136/15 square units.
