To find how much material was used in the manufacture of 24,000 dice, you can follow the steps below.
Step 1: Find the volume of one dice.
Since a dice is a cube, its volume (V) for edge (a) is:
[tex]\begin{gathered} V=a^3 \\ \end{gathered}[/tex]Knowing the measure of the edge (1/4 in), find the volume:
[tex]\begin{gathered} V=(\frac{1}{4})^3 \\ V=\frac{1^3}{4^3} \\ V=\frac{1}{64}in^3 \end{gathered}[/tex]Step 2: Find the volume of 24,000 dice.
Since the volume of one dice is 1/64 in³,
The volume of 24,000 dice is:
[tex]\begin{gathered} V=24,000\cdot\frac{1}{64} \\ V=\frac{24,000}{64} \\ V=375in^3 \end{gathered}[/tex]Answer: It is needed 375 in³ of material to manufacture 24,000 dice.
