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.)

(x, y, z) =

Answer 1

x = y = z = (√6)/3 cm ≈ 0.8165 cm

Explanation:

You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².

Largest volume

For a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.

Area

The total surface area of a cube with edge length s is ...

A = 6s²

Then the edge length of the desired cube is found from ...

4 = 6s²

s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator

s = √(6/9) = (√6)/3

The dimensions of the box are ...

x = y = z = (√6)/3 cm ≈ 0.8165 cm