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? Explai
2 answers:
Answer:
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
Step-by-step explanation:
Conceptual Analysis
Volume of the cube is the measure of its raised side the cube::
formula (1)
V: Volume of the cube in
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
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