Question
A water tank can be constructed with a metal top and two square ends that holds 16 cubic meter of water and requires 40 square meter of metal. find the dimensions of the water tank.
Answers
Steve
if the ends have side x, and the tank has height h,
x^2 h = 16
2x^2 + 4xh = 40
2x^2 + 4x(16/x^2) = 40
x^2 + 32/x = 20
x^3 - 20x + 32 = 0
(x-2)(x^2+2x-16) = 0
so, if x=2, the tank is 2x2x4
x^2 h = 16
2x^2 + 4xh = 40
2x^2 + 4x(16/x^2) = 40
x^2 + 32/x = 20
x^3 - 20x + 32 = 0
(x-2)(x^2+2x-16) = 0
so, if x=2, the tank is 2x2x4