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.

9x