## Calculating the Volume of a Model Building### Problem Statement1. 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): \(7xy + 14\)### TaskExplain 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 ExplanationThe 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 VolumeSubstitute 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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Answered: 1. A model building has dimensions as…

1. A model building has dimensions as shown. 2xy + 6 7xy+14 xy Explain how to calculate the volume of the model building. HINT: V = lwh

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 \(y\).

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