Total surface are

Given: Total surface area of cuboidal box (TSA) = 500 sq. unit

Breadth of cuboidal box (b) = 6 unit

Height of cuboidal box (h) = 5 unit

To find length (l) of the cuboidal box, recall total surface area of cuboid given by

TSA = 2 (lb + bh + hl)

Substituting given values in the formula, we get

500 = 2 (l×6 + 6×5 + 5×l)

⇒ 500 = 2 (6l + 30 + 5l)

⇒ 6l + 5l + 30 = 500/2

⇒ 11l + 30 = 250

⇒ 11l = 250 – 30 = 220

⇒ l = 220/11 = 20

Thus, length of the cuboidal box is 20 unit.