maths 20pts

4. In the figure, all the circles and the square touch one another. If the radius of the largest circle is 2, find the radius of the smallest circle.5. In the figure, ABCDEFGH is a cube. AB=12, M and N are the mid-points of AB and AD respectively. A plane through H,M and N cut the cube into 2 parts.
Find the volume of the larger part AFEHGQMNP.6. Let [x] denotes the largest integer not larger than x. e.g. [1.3]=1,[4]=4,[-1.3]=-2.
Let a_n=[n^0.5+(n+1)^0.5].Find the value of a_1+a_2+...+a_100.7. A positive integer n is ''good'' if n is not divisible by p^2 for all prime numbers p.
Let a_1,a_2,...,a_k be all the factors of 69300 which are ''good''.
Find the value of f(a_1)+f(a_2)+...+f(a_k) where f(X) denotes the sum of all the positive factors of X.

圖片參考：http://imgcld.yimg.com/8/n/HA08479696/o/701205230033013873408421.jpg