Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![## Calculating the Volume of a Model Building
### Problem Statement
1. A model building has dimensions as shown:
The diagram depicts a rectangular prism (box) with the following dimensions:
- Width (w): \(xy\)
- Length (l): \(2xy + 6\)
- Height (h): \(7xy + 14\)
### Task
Explain how to calculate the volume of the model building.
**Hint:** Use the formula for the volume of a rectangular prism:
\[ V = l \times w \times h \]
### Diagram Explanation
The diagram illustrates a rectangular box, with each dimension labeled with algebraic expressions in terms of \(x\) and \(y\). The width is denoted as \(xy\), the length is \(2xy + 6\), and the height is \(7xy + 14\). To find the volume, substitute these expressions into the volume formula.
### Calculating the Volume
Substitute the given expressions into the volume formula:
\[ V = (2xy + 6) \times (xy) \times (7xy + 14) \]
You will need to distribute and multiply these expressions to find the exact volume expression in terms of \(x\) and \(y\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc131e709-cc3e-4f0d-91ec-97e8c645b93d%2Fbc16b8b8-0f2b-461c-be48-92db316e4fc4%2F29e6mif_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Calculating the Volume of a Model Building
### Problem Statement
1. A model building has dimensions as shown:
The diagram depicts a rectangular prism (box) with the following dimensions:
- Width (w): \(xy\)
- Length (l): \(2xy + 6\)
- Height (h): \(7xy + 14\)
### Task
Explain how to calculate the volume of the model building.
**Hint:** Use the formula for the volume of a rectangular prism:
\[ V = l \times w \times h \]
### Diagram Explanation
The diagram illustrates a rectangular box, with each dimension labeled with algebraic expressions in terms of \(x\) and \(y\). The width is denoted as \(xy\), the length is \(2xy + 6\), and the height is \(7xy + 14\). To find the volume, substitute these expressions into the volume formula.
### Calculating the Volume
Substitute the given expressions into the volume formula:
\[ V = (2xy + 6) \times (xy) \times (7xy + 14) \]
You will need to distribute and multiply these expressions to find the exact volume expression in terms of \(x\) and \(y\).
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