The volume of a pyramid is given by the formula V= Bh where B is the area of its base and h is its height. The volume of the following pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters. cm (smaller value) |cm (larger value)
The volume of a pyramid is given by the formula V= Bh where B is the area of its base and h is its height. The volume of the following pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters. cm (smaller value) |cm (larger value)
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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![### Determining the Dimensions of a Pyramid Base
#### The volume of a pyramid is given by the formula:
\[ V = \frac{Bh}{3} \]
where \( B \) is the area of its base and \( h \) is its height.
#### Problem Statement:
The volume of the given pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters.
- **Volume (\( V \))**: 192 cm\(^3\)
- **Height (\( h \))**: 12 cm
Fill in the blanks for the base dimensions:
- __ cm (smaller value)
- __ cm (larger value)
---
#### Detailed Diagram Explanation:
The diagram below the text shows a rectangular-based pyramid. The key features labeled on the diagram include:
- The height (\( h \)) of the pyramid is shown with a vertical dashed line extending from the base to the apex of the pyramid.
- The rectangular base has two dimensions:
- \( x \) cm
- \( x + 2 \) cm
The \( x \) value represents one edge of the rectangular base, while \( x + 2 \) represents the other edge which is 2 cm longer than the first. An arrow annotation labeled "2" shows the extra length added to \( x \) for the longer side.
Given these details, the task is to solve for the values of \( x \) and \( x + 2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7d8b63c-f6b2-4537-9353-75fc012a2847%2Ff1797751-93ba-4b1a-af0f-b7e5ff8fb4b5%2Fhcwu42u_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Dimensions of a Pyramid Base
#### The volume of a pyramid is given by the formula:
\[ V = \frac{Bh}{3} \]
where \( B \) is the area of its base and \( h \) is its height.
#### Problem Statement:
The volume of the given pyramid is 192 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters.
- **Volume (\( V \))**: 192 cm\(^3\)
- **Height (\( h \))**: 12 cm
Fill in the blanks for the base dimensions:
- __ cm (smaller value)
- __ cm (larger value)
---
#### Detailed Diagram Explanation:
The diagram below the text shows a rectangular-based pyramid. The key features labeled on the diagram include:
- The height (\( h \)) of the pyramid is shown with a vertical dashed line extending from the base to the apex of the pyramid.
- The rectangular base has two dimensions:
- \( x \) cm
- \( x + 2 \) cm
The \( x \) value represents one edge of the rectangular base, while \( x + 2 \) represents the other edge which is 2 cm longer than the first. An arrow annotation labeled "2" shows the extra length added to \( x \) for the longer side.
Given these details, the task is to solve for the values of \( x \) and \( x + 2 \).
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