cuboid

Examples of cuboid in the following topics:

• Volumes

  • The volume of the cuboid with side lengths 4, 5, and 6 may be obtained in either of two ways.
  • of the constant function $1$ calculated on the cuboid itself.
  • of the function $z = f(x, y) = 5$ calculated in the region $D$ in the $xy$-plane, which is the base of the cuboid.
  • For example, if a rectangular base of such a cuboid is given via the $xy$ inequalities $3 \leq x \leq 7$, $4 \leq y \leq 10$, our above double integral now reads:

• Optimization in Several Variables

  • A packaging company needs cardboard boxes in rectangular cuboid shape with a given volume of 1000 cubic centimeters and would like to minimize the material cost for the boxes.
  • First of all, the material cost would be proportional to the surface area $S$ of the cuboid .
  • Mathematical optimization can be used to solve problems that involve finding the right size of a volume such as a cuboid.