Some challenging questions for the "challenging" students. =)


1. Triangle
Given a triangle where a unit circle is drawn with each vertex as the centre. Calculate the total area of the shaded region in the diagram above.


2. Star
Calculate the sum of the angles of the star shaded in the diagram above.


3. Cone
Consider a right circular cone.
Explain why when you cut the curved surface of the right circular cone and flatten it into two-dimension, you expect to get a sector (a sector is part of a circle like a shape of a pie of a pie chart).
Hence, show that the area of the curved surface of the right circular cone can be expressed as A=πrl, where r is the base radius of the cone, l is the length of the curved surface of the cone.


luv,
ms ang