LAr where L length and r If the volume (V) of a cylinder is calculated as V is the radius, express the length in terms of V, r, and r. %3D %3D How many kilometers are equal to 1.58 x 10° feet? If the density of silver is 10.5 / mL what is the mass of 1 cubic ft?
LAr where L length and r If the volume (V) of a cylinder is calculated as V is the radius, express the length in terms of V, r, and r. %3D %3D How many kilometers are equal to 1.58 x 10° feet? If the density of silver is 10.5 / mL what is the mass of 1 cubic ft?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Educational Website Content
#### Problem 1: Volume of a Cylinder
If the volume (V) of a cylinder is calculated as \( V = L \pi r^2 \) where \( L \) is the length and \( r \) is the radius, express the length in terms of \( V \), \( r \), and \( \pi \).
**Solution Steps:**
1. Start with the given formula:
\[ V = L \pi r^2 \]
2. To isolate \( L \), divide both sides of the equation by \( \pi r^2 \):
\[ L = \frac{V}{\pi r^2} \]
Thus, the length \( L \) can be expressed as:
\[ L = \frac{V}{\pi r^2} \]
---
#### Problem 2: Conversion of Feet to Kilometers
**Question:**
How many kilometers are equal to \( 1.58 \times 10^5 \) feet?
**Solution:**
1. Use the conversion factor: \( 1 \text{ foot} = 0.0003048 \text{ kilometers} \).
2. Multiply the given number of feet by the conversion factor:
\[ 1.58 \times 10^5 \text{ feet} \times 0.0003048 \text{ km/foot} \]
Calculating this:
\[ 1.58 \times 10^5 \times 0.0003048 = 48.16 \text{ kilometers} \]
So, \( 1.58 \times 10^5 \) feet is equal to 48.16 kilometers.
---
#### Problem 3: Density of Silver and Mass Calculation
**Question:**
If the density of silver is \( 10.5 \text{ g/mL} \) (or \( 10.5 \text{ g/cm}^3 \)), what is the mass of 1 cubic foot?
**Solution:**
1. Use the conversion between cubic feet and cubic centimeters: \( 1 \text{ cubic foot} = 28316.8 \text{ cubic centimeters (cm}^3) \).
2. Given the density \( \rho \) of silver is \( 10.5 \text{ g/cm}^3 \), multiply the density by the volume in cubic centimeters:
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Transcribed Image Text:### Educational Website Content
#### Problem 1: Volume of a Cylinder
If the volume (V) of a cylinder is calculated as \( V = L \pi r^2 \) where \( L \) is the length and \( r \) is the radius, express the length in terms of \( V \), \( r \), and \( \pi \).
**Solution Steps:**
1. Start with the given formula:
\[ V = L \pi r^2 \]
2. To isolate \( L \), divide both sides of the equation by \( \pi r^2 \):
\[ L = \frac{V}{\pi r^2} \]
Thus, the length \( L \) can be expressed as:
\[ L = \frac{V}{\pi r^2} \]
---
#### Problem 2: Conversion of Feet to Kilometers
**Question:**
How many kilometers are equal to \( 1.58 \times 10^5 \) feet?
**Solution:**
1. Use the conversion factor: \( 1 \text{ foot} = 0.0003048 \text{ kilometers} \).
2. Multiply the given number of feet by the conversion factor:
\[ 1.58 \times 10^5 \text{ feet} \times 0.0003048 \text{ km/foot} \]
Calculating this:
\[ 1.58 \times 10^5 \times 0.0003048 = 48.16 \text{ kilometers} \]
So, \( 1.58 \times 10^5 \) feet is equal to 48.16 kilometers.
---
#### Problem 3: Density of Silver and Mass Calculation
**Question:**
If the density of silver is \( 10.5 \text{ g/mL} \) (or \( 10.5 \text{ g/cm}^3 \)), what is the mass of 1 cubic foot?
**Solution:**
1. Use the conversion between cubic feet and cubic centimeters: \( 1 \text{ cubic foot} = 28316.8 \text{ cubic centimeters (cm}^3) \).
2. Given the density \( \rho \) of silver is \( 10.5 \text{ g/cm}^3 \), multiply the density by the volume in cubic centimeters:
\[ \
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