A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid?

We have that the length, width and height, are respectively L, W and H.

Now we know that the surface area of a solid rectangle is:

As = 2 * (L * W + W * H + L * H)

But we have to:

length increased by x% = L * (1 + x%) = L * (1 + x / 100)

width increased by y% = W * (1 + y%) = W * (1 + y / 100)

height increased by z% = H * (1 + z%) = H * (1 + z / 100)

Therefore the new area will be as follows:

AsN = 2 * [L * W * (1 + x / 100) * (1 + y / 100) + W * H * (1 + y / 100) * (1 + z / 100) + L * H * (1 + x / 100) * (1 + z / 100) ]

Percentage increase in the total surface area = [ (AsN - As) / As] * 100