Find the missing measurement for the figure to the nearest hundredth of a unit. Use a calculator, If needed. rectangular prism V = 620 ft 1= ft h = 음이 10 O 122R
Find the missing measurement for the figure to the nearest hundredth of a unit. Use a calculator, If needed. rectangular prism V = 620 ft 1= ft h = 음이 10 O 122R
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
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![**Problem 8: Find the missing measurement for the figure to the nearest hundredth of a unit. Use a calculator, if needed.**
**Figure: Rectangular Prism**
Given:
- Volume, \( V \) = 620 \( \text{ft}^3 \)
- Width, \( w \) = \( \frac{8}{4} \) ft
- Height, \( h \) = \( \frac{5}{7} \) ft
The given options for the length (\( l \)) are:
- \( \frac{12 \frac{2}{5}}{ft} \)
- \( \frac{12 \frac{1}{10}}{ft} \)
- \( \frac{12 \frac{7}{10}}{ft} \)
- \( \frac{12 \frac{3}{5}}{ft} \)
**Options:**
1. \(12 \frac{2}{5} \; ft \)
2. \(12 \frac{1}{10} \; ft \)
3. \(12 \frac{7}{10} \; ft \)
4. \(12 \frac{3}{5} \; ft \)
**Solution:**
To find the length (\( l \)) of the rectangular prism, use the formula for the volume of a rectangular prism:
\[ V = l \cdot w \cdot h \]
First, convert the given measurements to decimals:
- \( w \) = \( \frac{8}{4} \) = 2.00 feet
- \( h \) = \( \frac{5}{7} \approx 0.71 \) feet
Given \( V = 620 \, \text{ft}^3 \):
\[ 620 = l \cdot 2 \cdot 0.71 \]
Solving for \( l \):
\[ l = \frac{620}{2 \cdot 0.71} \]
\[ l \approx \frac{620}{1.42} \]
\[ l \approx 436.62 \]
Since this measurement does not fit any of the given options, there might be a mistake in the formulation of the options or the volume.
However, for educational purposes, select the option closest to the calculated length from the given choices.
**Note:**
The correct step-by-step calculations and checking should](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f1b5800-f045-4ccc-a00d-a1a031eae7ac%2F85e0b2be-5e13-48d7-958d-2af0008f5bef%2F6hg7l6q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 8: Find the missing measurement for the figure to the nearest hundredth of a unit. Use a calculator, if needed.**
**Figure: Rectangular Prism**
Given:
- Volume, \( V \) = 620 \( \text{ft}^3 \)
- Width, \( w \) = \( \frac{8}{4} \) ft
- Height, \( h \) = \( \frac{5}{7} \) ft
The given options for the length (\( l \)) are:
- \( \frac{12 \frac{2}{5}}{ft} \)
- \( \frac{12 \frac{1}{10}}{ft} \)
- \( \frac{12 \frac{7}{10}}{ft} \)
- \( \frac{12 \frac{3}{5}}{ft} \)
**Options:**
1. \(12 \frac{2}{5} \; ft \)
2. \(12 \frac{1}{10} \; ft \)
3. \(12 \frac{7}{10} \; ft \)
4. \(12 \frac{3}{5} \; ft \)
**Solution:**
To find the length (\( l \)) of the rectangular prism, use the formula for the volume of a rectangular prism:
\[ V = l \cdot w \cdot h \]
First, convert the given measurements to decimals:
- \( w \) = \( \frac{8}{4} \) = 2.00 feet
- \( h \) = \( \frac{5}{7} \approx 0.71 \) feet
Given \( V = 620 \, \text{ft}^3 \):
\[ 620 = l \cdot 2 \cdot 0.71 \]
Solving for \( l \):
\[ l = \frac{620}{2 \cdot 0.71} \]
\[ l \approx \frac{620}{1.42} \]
\[ l \approx 436.62 \]
Since this measurement does not fit any of the given options, there might be a mistake in the formulation of the options or the volume.
However, for educational purposes, select the option closest to the calculated length from the given choices.
**Note:**
The correct step-by-step calculations and checking should
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