Textbook Question
A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm3?
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Ch.1 - Matter, Measurement & Problem Solving
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217
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Table of contents
- Ch.1 - Matter, Measurement & Problem Solving90
- Ch.2 - Atoms & Elements94
- Ch.3 - Molecules and Compounds103
- Ch.4 - Chemical Reactions and Chemical Quantities46
- Ch.5 - Introduction to Solutions and Aqueous Solutions65
- Ch.6 - Gases100
- Ch.7 - Thermochemistry85
- Ch.8 - The Quantum-Mechanical Model of the Atom51
- Ch.9 - Periodic Properties of the Elements79
- Ch.10 - Chemical Bonding I: The Lewis Model70
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory68
- Ch.12 - Liquids, Solids & Intermolecular Forces44
- Ch.13 - Solids & Modern Materials42
- Ch.14 - Solutions77
- Ch.15 - Chemical Kinetics88
- Ch.16 - Chemical Equilibrium57
- Ch.17 - Acids and Bases121
- Ch.18 - Aqueous Ionic Equilibrium126
- Ch.19 - Free Energy & Thermodynamics80
- Ch.20 - Electrochemistry87
- Ch.21 - Radioactivity & Nuclear Chemistry61
- Ch.22 - Organic Chemistry114
Chapter 1, Problem 126
A solid aluminum sphere has a mass of 36 g. Use the density of aluminum to find the radius of the sphere in inches.
Verified step by step guidance1
Identify the density of aluminum, which is typically 2.70 g/cm³.
Use the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the volume of the sphere. Rearrange it to \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
Substitute the given mass (36 g) and the density of aluminum (2.70 g/cm³) into the volume formula to calculate the volume in cm³.
Use the formula for the volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) to solve for the radius \( r \). Rearrange it to \( r = \left(\frac{3V}{4\pi}\right)^{1/3} \).
Convert the radius from centimeters to inches using the conversion factor 1 inch = 2.54 cm.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density
Density is defined as mass per unit volume and is a key property of materials. For aluminum, the density is typically around 2.70 g/cm³. Understanding density allows us to relate the mass of an object to its volume, which is essential for solving problems involving geometric shapes like spheres.
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Density Concepts
Volume of a Sphere
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. This formula is crucial for determining the volume of the aluminum sphere based on its mass and density. By rearranging this formula, we can solve for the radius once we have the volume.
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Unit Conversion
Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, we need to convert the radius from centimeters to inches, as the final answer requires the radius in inches. Knowing the conversion factor (1 inch = 2.54 cm) is essential for accurate results.
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Related Practice
Textbook Question
The density of titanium is 4.51 g>cm3. What is the volume (in cubic inches) of 2.54 lb of titanium?
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An iceberg has a volume of 7655 ft2. What is the mass of the ice (in kg) composing the iceberg (at 0 °C)?
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The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 41 mi/gal in the city. How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda can? The volume of a soda can is 355 mL.
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Textbook Question
The density of iron is 7.86 g/cm3. What is its density in pounds per cubic inch (lb/in3)?
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