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Complete the chart below. In the last column, compute the ratio of the number in the third column divided by the number in the second column. Length of Side 1 2 3 4 5 6 7 8 9 10 n (if you can) Volume of Cubic Solid Volume of "Pyramid of Cubes" Volume of "Pyramid" Divided by Volume of Cubic Solid

Complete the chart below. In the last column, compute the ratio of the number in the third column divided by the number in the second column. Length of Side 1 2 3 4 5 6 7 8 9 10 n (if you can) Volume of Cubic Solid Volume of "Pyramid of Cubes" Volume of "Pyramid" Divided by Volume of Cubic Solid

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Volume Ratios of Cubic Solids and "Pyramid of Cubes" #### Instructions: Complete the chart below. In the last column, compute the ratio of the number in the third column divided by the number in the second column. | Length of Side | Volume of Cubic Solid | Volume of “Pyramid of Cubes” | Volume of “Pyramid” Divided by Volume of Cubic Solid | |----------------|-----------------------|-----------------------------|------------------------------------------------_____| | 1 | | | | | 2 | | | | | 3 | | | | | 4 | | | | | 5 | | | | | 6 | | | | | 7 | | | | | 8 | | | | | 9 | | | | | 10 | | | | | n (if you can) | | | | #### Explanation: 1. **Length of Side**: Represents the length of one side of the cubic solid. 2. **Volume of Cubic Solid**: The volume \(V\) of a cube is calculated using the formula \( V = s^3 \), where \( s \) is the length of a side. 3. **Volume of “Pyramid of Cubes”**: This column will contain the volume of a theoretical "pyramid" made up of cubes. 4. **Volume of “Pyramid” Divided by Volume of Cubic Solid**: Calculate the ratio by dividing the volume in the third column by the volume in the second column. Fill in the columns as per the lengths provided and calculate the necessary ratios.
Transcribed Image Text:### Volume Ratios of Cubic Solids and "Pyramid of Cubes" #### Instructions: Complete the chart below. In the last column, compute the ratio of the number in the third column divided by the number in the second column. | Length of Side | Volume of Cubic Solid | Volume of “Pyramid of Cubes” | Volume of “Pyramid” Divided by Volume of Cubic Solid | |----------------|-----------------------|-----------------------------|------------------------------------------------_____| | 1 | | | | | 2 | | | | | 3 | | | | | 4 | | | | | 5 | | | | | 6 | | | | | 7 | | | | | 8 | | | | | 9 | | | | | 10 | | | | | n (if you can) | | | | #### Explanation: 1. **Length of Side**: Represents the length of one side of the cubic solid. 2. **Volume of Cubic Solid**: The volume \(V\) of a cube is calculated using the formula \( V = s^3 \), where \( s \) is the length of a side. 3. **Volume of “Pyramid of Cubes”**: This column will contain the volume of a theoretical "pyramid" made up of cubes. 4. **Volume of “Pyramid” Divided by Volume of Cubic Solid**: Calculate the ratio by dividing the volume in the third column by the volume in the second column. Fill in the columns as per the lengths provided and calculate the necessary ratios.
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