Question

a box has a volume of 30 cubic centimeters. the box is filled with unit cubes, with no gaps or overlaps. each unit cube measures 1 centimeter in length, 1 centimeter in width, and 1 centimeter in height. how many unit cubes fill the box? 10 90 30 33

Explanation:

Step1: Recall volume formula for unit - cube

The volume of a unit cube with length $l = 1$ cm, width $w=1$ cm and height $h = 1$ cm is $V_{unit - cube}=l\times w\times h=1\times1\times1 = 1$ $cm^{3}$.

Step2: Calculate number of unit - cubes

The number of unit - cubes $n$ that fill the box is given by the ratio of the volume of the box $V_{box}$ to the volume of a unit - cube $V_{unit - cube}$. Given $V_{box}=30$ $cm^{3}$ and $V_{unit - cube}=1$ $cm^{3}$, then $n=\frac{V_{box}}{V_{unit - cube}}=\frac{30}{1}=30$.

Answer:

30