Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
Find the volume for the rectangular prism. Write your answer in simplest form.
![**Volume of a Rectangular Prism Calculation**
To find the volume of the rectangular prism, multiply its length, width, and height. Make sure to provide the answer in simplest form.
### Diagram Explanation:
The provided diagram shows a rectangular prism with the labeled dimensions:
- Length: \( \frac{5}{7} \) ft
- Width: \( \frac{1}{8} \) ft
- Height: \( \frac{8}{9} \) ft
### Formula to Calculate Volume:
\[ V = \text{length} \times \text{width} \times \text{height} \]
### Applying the Dimensions:
\[ V = \left(\frac{5}{7} \, \text{ft} \right) \times \left(\frac{1}{8} \, \text{ft} \right) \times \left(\frac{8}{9} \, \text{ft} \right) \]
### Simplifying the Multiplication:
1. Multiply the numerators:
\[ 5 \times 1 \times 8 = 40 \]
2. Multiply the denominators:
\[ 7 \times 8 \times 9 = 504 \]
3. Combine these into a single fraction:
\[ \frac{40}{504} \]
4. Simplify the fraction:
\[ \frac{40 \div 8}{504 \div 8} = \frac{5}{63} \]
### Final Volume:
\[ V = \frac{5}{63} \, \text{ft}^3 \]
Hence, the volume of the rectangular prism is \(\frac{5}{63} \, \text{ft}^3 \).
Please enter your answer in the provided box on the educational website:
\[ \boxed{\frac{5}{63}} \, \text{ft}^3 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8d11063-2bda-4ec0-87e2-714d5471412b%2F7e39fc60-d0ab-4d8c-9045-4641362c7bc2%2Fwh08f2s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume of a Rectangular Prism Calculation**
To find the volume of the rectangular prism, multiply its length, width, and height. Make sure to provide the answer in simplest form.
### Diagram Explanation:
The provided diagram shows a rectangular prism with the labeled dimensions:
- Length: \( \frac{5}{7} \) ft
- Width: \( \frac{1}{8} \) ft
- Height: \( \frac{8}{9} \) ft
### Formula to Calculate Volume:
\[ V = \text{length} \times \text{width} \times \text{height} \]
### Applying the Dimensions:
\[ V = \left(\frac{5}{7} \, \text{ft} \right) \times \left(\frac{1}{8} \, \text{ft} \right) \times \left(\frac{8}{9} \, \text{ft} \right) \]
### Simplifying the Multiplication:
1. Multiply the numerators:
\[ 5 \times 1 \times 8 = 40 \]
2. Multiply the denominators:
\[ 7 \times 8 \times 9 = 504 \]
3. Combine these into a single fraction:
\[ \frac{40}{504} \]
4. Simplify the fraction:
\[ \frac{40 \div 8}{504 \div 8} = \frac{5}{63} \]
### Final Volume:
\[ V = \frac{5}{63} \, \text{ft}^3 \]
Hence, the volume of the rectangular prism is \(\frac{5}{63} \, \text{ft}^3 \).
Please enter your answer in the provided box on the educational website:
\[ \boxed{\frac{5}{63}} \, \text{ft}^3 \]
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