Mathematics Question and Solution
Let the radius of the semi circle be 3 units.
Calculating area Red.
Area red will be;
2(area triangle of two length 3 units and 1 unit, and angle (cos–¹(⅓)), angle they form) + area sector of radius 3 units and angle (180-2cos–¹(⅓)).
= ½(2(1*3sin(cos–¹(⅓)))) + ((180-2cos–¹(⅓))*9π÷360)
= 3sin(cos–¹(⅓)) + ((180-2cos–¹(⅓))*π÷40)
= 5.88695930984 square units.
Area of the semi circle is;
= ½(9π)
= 4.5π square units.
Therefore percent of the shaded area from the whole semi circle is;
((5.88695930984)/(4.5π)) x 100
= 41.641718842%
