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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
7.5cm^(3). What is the volume of the waste generated by creating the die from the cube in
cm^(3) ?

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 $(\mathrm{cm})$ . The volume of the final die is $7.5 \mathrm{~cm}^{3}$ . What is the volume of the waste generated by creating the die from the cube in $\mathrm{cm}^{3}$ ?

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Scale drawings: word problems

Full solution

Q. 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

(\mathrm{cm})

. The volume of the final die is

7.5 \mathrm{~cm}^{3}

. What is the volume of the waste generated by creating the die from the cube in

\mathrm{cm}^{3}

?

Calculate volume of original cube: The volume of a cube is given by the formula $V = s^3$ , where $s$ is the length of a side of the cube. $\newline$ $V_{\text{cube}} = 2 \, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^3$
Determine volume of final die: The volume of the final die is given as $7.5\,\text{cm}^3$ .
Calculate volume of waste material: The volume of the waste is the difference between the volume of the original cube and the volume of the final die. $\newline$ $\text{Volume}_{\text{waste}} = \text{V}_{\text{cube}} - \text{V}_{\text{die}}$ $\newline$ $\text{Volume}_{\text{waste}} = 8 \, \text{cm}^3 - 7.5 \, \text{cm}^3 = 0.5 \, \text{cm}^3$

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