Intermediate college algebra
posted by Jen .
Beer cans are right circular cylinders. My algebraic ale and logarithmic lager cans, from snide brewery, have dimensional units called brewskis. The have a volume (in cubic brewskis) equal to the solution of the number of grams of radium 226 remaining after 4860 years when the original sample contained 648 pi grams. The height divided by the radius of my beer can is equal to the solution of: log6 W + log6 (w+9)=2. Do not round pi while finding the surface area of my beer can.

I find dumb and cutesy word problems like this very irritating, and will not answer them.
Tell your teacher to give you problems that are meaningful and serve a purpose. 
especially since you have to go look up the halflife of ^{226}Ra, which is 1601 years
however, I'm both bored and not proud, so here goes:
v = 648π*(1/2)^(4860/1601) =~ 79π
h/r = w = 3
πr^2*h = 79π
πr^2(3r) = 79π
3r^3 = 79
r = 2.98
a = 2πr(r+h) = 2π*2.98(2.98*4) =~ 71π 
I see that the radium decay is suspiciously close to 3 halflives.
If that was what was wanted, then
v = 81π
r = 3
a = 72π