Question

A gold bar is similar in shape to a rectangular prism. A gold bar is approximately 7 1 6 in. x2 in. x 1 in. If the value of gold is $1,417 per ounce, about how much 8 2 is one gold bar worth? Use the formula w ~ 11.15n, where w is the weight in ounces and n= volume in cubic inches, to find the weight in ounces. Explain how you found your answer.

Answer 1

ANSWER and EXPLANATION

We want to find how much the gold bar is worth.

First, we have to find the volume of the gold bar.

The volume of a rectangular prism is:

`\begin{gathered} V=L\cdot W\cdot H \\ L=\text{length;} \\ W=\text{width;} \\ H=\text{height} \end{gathered}`

Therefore, the volume of the gold bar is:

`\begin{gathered} V=6\cdot2(7)/(8)\cdot1(1)/(2) \\ V=6\cdot(23)/(8)\cdot(3)/(2) \\ V=25.88\text{ cubic inches} \end{gathered}`

Now, convert the volume to weight y using:

`\begin{gathered} w\approx11.15n \\ \text{where w = weight in ounces; n = volume in cubic inches} \end{gathered}`

Therefore, its weight is:

`\begin{gathered} w\approx11.15\cdot25.88 \\ w\approx288.56\text{ ounces} \end{gathered}`

Finally, multiple the weght by the value of gold:

`\begin{gathered} \text{Worth}=288.56\cdot1417 \\ \text{Worth}=\text{ \$}408,889.52 \end{gathered}`

Therefore, the volume of the gold bar is about 25.88 in³, so the weight is approximately 288.56 ounces. So one gold bar is worth about $408,889.52