Α = 2·pi·x·(x + h)
4500 = pi·x^2·h----> h = 4500/(pi·x^2)
Α = 2·pi·x·(x + 4500/(pi·x^2))
Α = 2·pi·x^2 + 9000/x----> Α = 2·(pi·x^3 + 4500)/x
Α = (2·pi·x^3 + 9000)/x
a)
V(h,x) = pi*x²*h
b)
At(h,x) = 2pi*x² + 2pi*x*h
c)
4500*10^-6 = V = pi*x²*h ---> h(cm) = 4500/(pi*x²)
d)
At(x,h) = 2pi*x² + 2pi*x*4500/(pi*x²) = 2pi*x² + 2pi*4500*x/(pi*x²) = (2pi²*x^4 +9000*pi*x)/(pi*x²) = (2pi*x³+ 9000)/x = A(x) cvd.
Sì