Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Orange.
Radius of the circle, r is;
(5-r)²=18-18cos(180-2atan(4/3))
(5-r)²=12.96
5-r=√(12.96)
5-r=3.6
Therefore;
r = 1.4 units.
Area orange is;
Area sector with radius 1.4 units and angle atan(4/3)° - Area triangle with two lengths 1.4 units and 1.13836187945 units, and angle ½(atan(4/3))°, the angle they form.
= 1.4²π(atan(4/3))/360 - ½(1.4*1.13836187945)sin(½(atan(4/3)))
= 0.90874931364 - 0.3563636363
= 0.55238567728 square units.
