Question

Beer cans are right circular cylinders. My Mathematical Mead, my Polynomial Pilsner, and my Square-Root Stout cans from the Schmidt Brewery, have dimensional units called "brewskies". Using the zero product rule, they have a volume (in cubic brewskies) equal to a solution of the function:
f(x)=-24πx²+3x+x³-72π (where π=pi).
The height divided by the radius of my beer can is equal to the solution of :
(2k+3)^½+(k+1)^½=5.
Do not round π while finding the volume, diameter, and height of my beer can.

Answer 1

v = x^3 - 24πx^2 + 3x - 72π
= x(x^2+3) - 24π(x^2+3)
= (x-24π)(x^2+3)
The only real solution (required when sober) is x=24π

Now, we need to solve for k:
√(2k+3) + √(k+1) = 5
k=3

so, h/r = 3, meaning h = 3r
v = 24π = πr^2h = 3πr^3
24 = 3r^3, so r=2

I figure you can work out the answers to the questions now...