76.00 lb flask or mercury costs $137, the density of mercury is 13.534 g/cm^3. determine the price of one cm^3 of mercury 

To determine the price of one cubic centimeter (cm³) of mercury, we need to convert the price of the mercury flask into a cost per cm³.

### Step 1: Convert the weight of the flask to grams
The weight of the flask is given as 76.00 lb. We need to convert this weight into grams.

1 lb = 453.592 grams, so:
\[
76.00 \, \text{lb} \times 453.592 \, \text{g/lb} = 34473.03 \, \text{grams}
\]

### Step 2: Calculate the volume of mercury in cm³
The density of mercury is given as 13.534 g/cm³. Using the formula for density, which is:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]
We can rearrange it to find the volume:
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{34473.03 \, \text{grams}}{13.534 \, \text{g/cm}^3} = 2547.95 \, \text{cm}^3
\]

### Step 3: Calculate the price per cm³ of mercury
The total cost of the mercury flask is $137, so the price per cm³ is:
\[
\text{Price per cm}^3 = \frac{137}{2547.95} \approx 0.0538 \, \text{\$/cm}^3
\]

Thus, the price of one cubic centimeter (cm³) of mercury is approximately **$0.0538**.

Would you like further details or have any questions?

Here are some related questions:
1. How would the price change if the density of mercury was slightly different?
2. What would be the cost per cm³ if the flask weighed 100 lbs instead of 76 lbs?
3. How does the density of mercury compare to other common metals like gold or lead?
4. What would the total cost be for a 10 cm³ sample of mercury?
5. How can this problem be applied in a real-world scenario, like in a laboratory setting?

**Tip:** Always remember to use the correct units and conversion factors when dealing with mass, volume, and density problems.

Learn how to determine the price of one cubic centimeter (cm³) of mercury with a step-by-step solution. This problem involves converting units, calculating density, and finding cost per volume unit. Suitable for high school students.

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