Question

Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-square-inch cubes inside the box? Explain.

Answer 1

No she would only be able to fit 729, because 9^2 equals 81, and 81*9 equals 729.

Answer 2

Since the total volume of one-inch cubes (Vt₂) is greater than the volume of Maria's box (V₁), then, the 1000 1-inch cubes do not fit in Maria's box

Explanation:

Conceptual Analysis

Volume of the cube is the measure of its raised side the cube::

`V=a^(3)` formula (1)

V: Volume of the cube in
`in^(3)`

a: Side the cube in inches

Nomenclature

V₁:Maria's box volume

V₂: Volume of cubes measuring 1 inch

a₁:measure of the side of Maria's box

a₂:side measurement of cubes measuring 1 inch

n₁:number of cubes that Maria has

n₂:Number of cubes measuring 1 inch

Known data:

a₁=9inches

a₂=1 inches

n₁= 1

n₂= 1000

Problem development

We replace the data in formula (1) to calculate volume:

V₁=9³=729 in³

V₂=1³=1in³

Vt₂=1*1000=1000 in³:Total volume of 1 inch cubes

Since the total volume of one-inch cubes (Vt₂) is greater than the volume of Maria's box (V₁), then, the 1000 1-inch cubes do not fit in Maria's box