Question

a sheet of area 27m2 is used to make an open tank with square base then find the base area (in m2) of tank such that volume of this tank is maximum

Answer 1

Answer:

Let length = x and height = y

Given x2 + 4xy = 40

⇒ y = (40 – x2)/4x

Now, Volume = V = x2 y = x2((40 – x2)/4x) = x(40 – x2) = 40x – x3

⇒ dV/dx = 40 – 3x2

⇒ d2V/dx2 = –6x For max or min,

dV/dx = 0 gives x = √(40/3)

So, at x = √(40/3), d2V/dx2 < 0

Thus, volume is maximum

Therefore,

length = x = √(40/3) and height = y = √(10/3)