How much metal is needed to cast a cubical metal box with an outer side $10 inches$ long if the thickness of its walls should be exactly $2 inches$ ?

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Solution

Step 1. Find the outer volume of a cubical metal box.
The length of the outer side of a cubical metal box is $10 inches$ .
Formula to find the volume of the cubical box is $Volume = {(side)}^{3}$ .
The outer volume of the cubical metal box is as follows:
$\begin{array}{rcl} Volume & = & {(10)}^{3} \\ = & 1000 {inches}^{3} \end{array}$
Step 2. Find the inner volume of a cubical metal box.
The thickness of the wall of the metal box is $2 inches.$
So, the length of the inner side of a cubical metal box is $10 - 2 = 8 inches$ .
The inner volume of the cubical metal box is as follows:
$\begin{array}{rcl} Volume & = & (8^{3}) \\ = & 512 {inches}^{3} \end{array}$
Step 3. Find how much metal is needed to cast a cubical metal box.
Subtract the inner volume from the outer volume of the cubical metal box:
$1000 - 512 = 488 {inches}^{3}$
Therefore, the metal is needed to cast a cubical metal box is $488 {inches}^{3}$ .

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How much metal is needed to cast a cubical metal box with outer side $10 inches$ long if the thickness of its walls should be exactly $2 inches$ ?

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