Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let R be radius of the inscribed circle.
Calculating r.
√(100-25) = r+√(25+r²)
r = ⅓(5√(3)) cm.
Therefore;
Area Shaded as a single fraction in terms of π is;
Area sector with radius 10cm and angle 30° - Area triangle with height 7.40536184888 cm and base ⅓(10√(3)sin30) cm.
= (30*π*100÷360) - (0.5*7.40536184888*⅓(10√(3)sin30))
= ⅓(25π) - (889749425√(3)/144179222)
= ( 3604480550π- 2669248275√(3))/ 432537666 cm²
= 15.49121963767 cm²
