Question

A cuboid of dimensions a × b × c, with a < b < c, has to be cut into two equal parts across one of its sides. Which side should be chosen to get maximum increase in surface area?​

Answer 1

Given:

Dimensions of the cuboid =  a × b × c

a < b< c

To find:

Which side should be chosen to get maximum increase in surface area?​

Solution:

The cuboid can be cut from the shortest side, i.e. the c side,

Because then the surface are of the two small cubes will be the largest.

Surface are = 2*lw + 2*lh + 2*hw

where l = length of cuboid

w = width

h = height

Surface area = 2*ab + 2*bc/2 + 2*ac/2

= 2ab + bc + ac which is the maximum.

Therefore side c should be chosen to get maximum increase in surface area.