Roberto wants to build a wooden box with a volume of 8 cubic feet. How many different boxes, all with whole number dimensions and a different size base, will have a volume of 8 cubic feet?

Three different boxes will have a volume of 8 cubic feet

Step-by-step explanation:

The formula for the volume of box = Length, l * Breadth, b * Height, h

Where, the base size = l * b

The number of different boxes are;

l * b * h

1 * 1 * 8

1 * 2 * 4

2 * 4 * 1

2 * 2 * 2

1 * 8 * 1

Whereby the base are to be different, we note that the following;

1 * 8 * 1 = 1 * 1 * 8

1 * 2 * 4 = 2 * 4 * 1

Hence the different boxes with different bases that will have a volume of 8 ft³ are;

h * b * l

1) 1 * 1 * 8

2) 1 * 2 * 4

3) 2 * 2 * 2

Which are three different boxes with dimensions;

Box 1: Length = 8 ft, breadth = 1 ft., and height = 1 ft

Box 2: Length = 4 ft, breadth = 2 ft., and height = 1 ft

Box 3: Length = 2 ft, breadth = 2 ft., and height = 2 ft.