Homework Soursea company is constructing an open top square based rectangul
a company is constructing an open top square based rectangular metal tank with a volume of 30ft^3
What dimensions yield the minimum surface area
What dimensions yield the minimum surface area
Solution
V = 30 = b^2 * h h = 30 / b^2 Surface area A = b^2 + 4 bh A = b^2 + 4b * (30/b^2) A = b^2 + 120 /b A\' = 2b - 120 / b^2 2b - 120 / b^2 = 0 (2 (b^3-55)) / b^2 = 0 b^3 = 55 b = 3.8 h= 30 / 3.8^2 = 2.08 3.8/2.08=1.83 Surface area is minimized when height is 1.83 the base length.
