Question

Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box).

Answer 1

Answer:

The dimensions of the rectangular box, x = y = z = 0.817 cm

Step-by-step explanation:

Given;

total surface area of the rectangular box or cuboid = 4 cm²

A rectangular box with largest volume  is a cube.

The total surface area of a cube = 6 times  square of one edge length.

Let the edge length = given dimensions,  x, y, z

x = y = z

6x² = 4

x² = 4/6

$x =\sqrt{\frac{4}{6} }\\\\ x = \frac{2}{\sqrt{6} } \ cm \ = 0.817 \ cm$

Therefore, the dimensions of the rectangular box, x = y = z = 0.817 cm