Question

1. A sheet of area 40 m^2used to make an open tank with a square base, then find the
dimensions of the base such that volume of this tank is maximum​

Answer 1

Answer:

Hence, dimensions of the base such that volume of this tank is maximum = √(40/3) m

Explanation :

Let side of square tank be x .

And, height be y .

Then, Volume = x²y .

And, Surface area = x² + 4xy .

→ 40 = x² + 4xy .

→ y = ( 40 - x² ) / 4x .

Then, V(y) = x² ( 40 - x² )/4x.

= x( 40 - x² ) / 4 .

Now, dV/dx = ( 40 - 3x² )/4 .

And, d²V/dx² = -3x/2 = Vmax.

Therefore, dV/dx = 0 .

→ ( 40 - 3x² )/4 = 0 .

→ 40 - 3x² = 0 .

→ 3x² = 40 .

→ x² = 40/3 .

x = √(40/3) m.

Hence, dimensions of the base such that volume of this tank is maximum = √(40/3) m

Answer 2

Refer to the attached image ☺️