Senior Mathematics Competition

Warsaw 2011
 

Our senior team is to be congratulated on a fine performance in the international mathematics contest.  The three members of the ISH team came 18th out of 63 teams from all over Europe and North Africa Here are a couple of geometry questions which our team solved in about 10 minutes.

Here are a couple of geometry questions which our team solved in about 10 minutes.

 

 

The radius of the sphere is 1cm. The radius of the base of the cone is 2cm. What is the height of the cone?

 

 

 

The radius of the semicircle is 1cm. The square has the same area as triangle PQR.   What is the length of PQ?