Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 75c

Chapter 1, Problem 75c

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (c) How much money would this stack contain?

Verified step by step guidance

Determine the volume of a single quarter using its thickness and the formula for the volume of a cylinder: $V = \pi r^2 h$, where $h$ is the thickness and $r$ is the radius.

Calculate the mass of a single quarter, which is given as 5.67 g.

Find the total mass of the stack of quarters by dividing the total mass of the stack by the mass of a single quarter.

Calculate the number of quarters in the stack by dividing the total mass of the stack by the mass of a single quarter.

Determine the total monetary value by multiplying the number of quarters by the value of a single quarter, which is $0.25.

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Key Concepts

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

Mass and Volume Relationship

Understanding the relationship between mass and volume is crucial in this context. The mass of the quarter is given, and knowing the density of the material can help calculate the volume of a single quarter. This relationship is foundational in determining how many quarters can fit into a given space.

Stack Height Calculation

To find out how much money a stack of quarters contains, one must calculate the total height of the stack. Given the thickness of a single quarter, the total height can be determined by multiplying the number of quarters by the thickness. This calculation is essential for determining the monetary value of the stack.

Monetary Value of Quarters

Each U.S. quarter has a fixed monetary value of 25 cents. To find the total amount of money in a stack of quarters, one must multiply the number of quarters by this value. This concept ties together the physical properties of the quarters with their economic value, allowing for a complete answer to the question.

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Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick. (a) How many quarters would have to be stacked to reach 575 ft, the height of the Washington Monument?

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Textbook Question

The U.S. quarter has a mass of 5.67 g and is approximately 1.55 mm thick.(d) The U.S. National Debt Clock showed the outstanding public debt to be $16,213,166,914,811 on October 28, 2012. How many stacks like the one described would be necessary to pay off this debt?

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