Nah, I'm doing the intermediate. I don't think they vary too much in difficulty though as I've noticed that question 30 in the intermediate is around question 28/29 in senior. I've also noticed that their are quite a few common questions each year.
The bottom of the circle travels half a circumference, i.e. pi*r
Could you please post your working si2136.
Exactly six of these 'unusually shaped portions' fit into the regular octahedron by symmetry (one at each vertex) so the volume of one portion is one-sixth the volume of the octahedron, ie. 1/6 * 120 = 20
Let f(n) be the quantity for a given n. It is pretty easy to show that f(mn)=f(m)f(n) for coprime m and n (a and b each uniquely factorise into the product of something that divides m and something that divides n), and also that f(p^n)=(n+1)(n+2)/2 by manual counting.
Notice that the unshaded area must also be divided in half. By drawing a diagram with the centres of the circles and the perpendiculars from the centres to the dividing line, it can be shown that the line must pass through the midpoint between the centres of the spheres. Letting P be the origin and then have a normal x-y plane, M = (5/2, 1) and also passes through C = (6,2). Then, find the line MN and substitute x=0 to obtian y = 2/7, which is A.
For the third question from the top,
You seem a great chance for a medal. I'm pretty confident I got 87 points and I'm hoping that one of the 3 I guessed were correct.
Haahaha maybe just miss it and get HD
Depends on how the cohort goes. There were 3 others that I had to guess that were between 2 choices.
Have questions about the area of a hexagon or a n-gon?
