Calculate the value of the silver in the American Silver Eagle coin, assuming its thickness is uniform, given that it has a diameter of 41 mm, a thickness of 2.5 mm, a silver density of 10.5 g/cm3, and the approximate market price of silver is $0.51 per gram.

Verified step by step guidance

Convert the diameter and thickness of the coin from millimeters to centimeters to match the units of density. Remember that 1 cm = 10 mm.

Calculate the volume of the coin using the formula for the volume of a cylinder: $ V = \pi r^2 h $, where $ r $ is the radius and $ h $ is the height (thickness) of the cylinder.

Use the density formula $ \text{Density} = \frac{\text{Mass}}{\text{Volume}} $ to find the mass of the silver in the coin. Rearrange the formula to solve for mass: $ \text{Mass} = \text{Density} \times \text{Volume} $.

Calculate the mass of the silver in grams using the density of silver and the volume of the coin obtained in the previous steps.

Determine the value of the silver in the coin by multiplying the mass of the silver by the market price per gram of silver.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Volume of a Cylinder

The American Silver Eagle coin can be approximated as a cylinder, where the volume is calculated using the formula V = πr²h. Here, r is the radius (half the diameter), and h is the height (thickness). Understanding how to calculate the volume is essential for determining the amount of silver in the coin.

Density and Mass Relationship

Density is defined as mass per unit volume (density = mass/volume). By knowing the density of silver and the volume of the coin, one can calculate the mass of silver in the coin. This relationship is crucial for converting the volume of silver into a tangible mass value.

Market Price of Silver

The market price of silver is the cost per gram of silver in the market. To find the total value of the silver in the coin, the mass of silver calculated from the previous concepts is multiplied by the market price. Understanding this concept allows for the final valuation of the silver content in the coin.

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The first atoms of seaborgium (Sg) were identified in 1974. The longest-lived isotope of Sg has a mass number of 266. (a) How many protons, electrons, and neutrons are in an ²⁶⁶Sg atom?

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The first atoms of seaborgium (Sg) were identified in 1974. The longest-lived isotope of Sg has a mass number of 266. (b) Atoms of Sg are very unstable, and it is therefore difficult to study this element's properties. Based on the position of Sg in the periodic table, what element should it most closely resemble in its chemical properties?

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From the molecular structures shown here, identify the one that corresponds to each of the following species: (a) chlorine gas; (b) propane; (c) nitrate ion; (d) sulfur trioxide; (e) methyl chloride, CH3Cl.

Textbook Question

Fill in the blanks in the following table:

Cation Anion Formula Name

Lithium oxide

Fe²⁺ PO₄^3-

Al₂(SO₄)₃

Copper(II) nitrate

Cr³⁺I⁻

MnClO₂

Ammonium carbonate

Zinc perchlorate

Complete the first column of the table.