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
![**Exploring the Relationship Between Base Area and Volume of a Prism**
**Question:**
Does doubling the base area of a prism double its volume? Use the figure below to help you answer the question.
**Diagram Explanation:**
The figure shows a rectangular prism with the following dimensions:
- Height: 6 cm
- Length: 12 cm
- Width: 8 cm
The base of the prism is a rectangle with dimensions 12 cm by 8 cm. The volume of the prism is determined by the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
First, calculate the base area:
\[ \text{Base Area} = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2 \]
Now, calculate the volume:
\[ \text{Volume} = 96 \, \text{cm}^2 \times 6 \, \text{cm} = 576 \, \text{cm}^3 \]
To explore the effect of doubling the base area, imagine modifying the base dimensions or shape so that the area becomes:
\[ 2 \times 96 \, \text{cm}^2 = 192 \, \text{cm}^2 \]
Keep the height constant at 6 cm and recalculate the volume:
\[ \text{New Volume} = 192 \, \text{cm}^2 \times 6 \, \text{cm} = 1152 \, \text{cm}^3 \]
**Conclusion:**
Doubling the base area of a prism also doubles its volume, assuming the height remains unchanged.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df48705-4238-4207-b57b-19ed7b40517e%2F19ec43a8-e551-4f36-a10b-86a4c2bcc065%2Fkgfy7wj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exploring the Relationship Between Base Area and Volume of a Prism**
**Question:**
Does doubling the base area of a prism double its volume? Use the figure below to help you answer the question.
**Diagram Explanation:**
The figure shows a rectangular prism with the following dimensions:
- Height: 6 cm
- Length: 12 cm
- Width: 8 cm
The base of the prism is a rectangle with dimensions 12 cm by 8 cm. The volume of the prism is determined by the formula:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
First, calculate the base area:
\[ \text{Base Area} = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2 \]
Now, calculate the volume:
\[ \text{Volume} = 96 \, \text{cm}^2 \times 6 \, \text{cm} = 576 \, \text{cm}^3 \]
To explore the effect of doubling the base area, imagine modifying the base dimensions or shape so that the area becomes:
\[ 2 \times 96 \, \text{cm}^2 = 192 \, \text{cm}^2 \]
Keep the height constant at 6 cm and recalculate the volume:
\[ \text{New Volume} = 192 \, \text{cm}^2 \times 6 \, \text{cm} = 1152 \, \text{cm}^3 \]
**Conclusion:**
Doubling the base area of a prism also doubles its volume, assuming the height remains unchanged.
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