Question

a die is created by smoothing the corners of a plastic cube and carving indented pips. the original cube had an edge length of 2 centimeters (cm). the volume of the final die is 7.5 cm³. what is the volume of the waste generated by creating the die from the cube in cm³?

Explanation:

Step1: Calculate cube volume

The volume formula for a cube is $V = a^{3}$, where $a = 2$ cm. So $V_{cube}=2^{3}=8$ $cm^{3}$.

Step2: Calculate waste volume

The waste volume $V_{waste}$ is the difference between the cube volume and the die - volume. $V_{waste}=V_{cube}-V_{die}$. Given $V_{die} = 7.5$ $cm^{3}$, then $V_{waste}=8 - 7.5=0.5$ $cm^{3}$.

Answer:

$0.5$