Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 156 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions? The length of the square-end edge is The box height is in. The greatest volume of the box is ☐ in³. in.

When the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the length of each edge of the original cube?

The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?

As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?