A penny has a density of 7.20 g/cm3. How much copper is contained in a penny that is 2.50% (by weight) of copper? Recall that a penny has a diameter of 19.05 mm and a thickness of 1.52 mm.
The Correct Answer and Explanation is :
The mass of copper contained in the penny is approximately 0.078 g.
Explanation:
To determine the amount of copper in the penny, we first need to calculate the volume, then find the total mass using density, and finally determine the fraction of copper.
- Convert Dimensions to Centimeters
Since density is given in g/cm³, we convert the penny’s dimensions from mm to cm:
- Diameter: 19.05 mm = 1.905 cm
- Thickness: 1.52 mm = 0.152 cm
- Radius: 1.905 cm ÷ 2 = 0.9525 cm
- Calculate the Volume of the Penny
The volume of a cylinder is given by:
[
V = \pi r^2 h
]
Substituting values:
[
V = \pi (0.9525)^2 (0.152)
]
[
V \approx 0.434 cm^3
] - Find the Mass of the Penny
Using the formula:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
[
\text{Mass} = (7.20 \text{ g/cm}^3) \times (0.434 \text{ cm}^3)
]
[
\text{Mass} \approx 3.13 \text{ g}
] - Determine the Mass of Copper
Since the penny is 2.50% copper by weight, we multiply:
[
\text{Mass of Copper} = 3.13 \times \frac{2.50}{100}
]
[
\text{Mass of Copper} \approx 0.078 \text{ g}
]
Thus, the penny contains approximately 0.078 g of copper. Now, I will generate an image to visualize this calculation.
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