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
![**Problem Statement:**
How many square feet of sheet metal are needed to form the trough shown in the figure below?
**Diagram Explanation:**
The figure depicts a trough with the following specifications:
- The shape of the trough has a half-circle cross-section.
- The diameter of the half-circle is labeled as \(10.0\) inches.
- The length of the trough is labeled as \(12\) feet.
**Conversion Information:**
To solve the problem, note that the dimensions are given in both inches and feet. Conversion between these units will be necessary to calculate the total area correctly.
**Calculation Process:**
1. **Convert the Diameter to Feet:**
- Since 1 foot = 12 inches, convert 10 inches to feet: \(10 \text{ inches} = \frac{10}{12} \text{ feet}\).
2. **Calculate the Radius:**
- The radius \(r\) is half of the diameter: \(r = \frac{5}{12} \text{ feet}\).
3. **Calculate the Area of the Half-Circle Cross-Section:**
- The area \(A\) of a circle is \(\pi r^2\). Thus, the area of a half-circle is \(\frac{\pi r^2}{2}\).
4. **Calculate the Lateral Surface Area of the Trough:**
- Multiply the area of the half-circle by the length of the trough to find the total lateral surface area in square feet.
5. **Final Answer:**
- Calculate and fill in the blank for square feet of sheet metal needed.
\[ \_\_\_\_\_ \text{ ft}^2 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5bdb4ac-6ebf-4e62-b2b9-ef945c39bf06%2F8f4d28d4-0543-415b-890c-0d7bc6e64990%2Fe2delre_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
How many square feet of sheet metal are needed to form the trough shown in the figure below?
**Diagram Explanation:**
The figure depicts a trough with the following specifications:
- The shape of the trough has a half-circle cross-section.
- The diameter of the half-circle is labeled as \(10.0\) inches.
- The length of the trough is labeled as \(12\) feet.
**Conversion Information:**
To solve the problem, note that the dimensions are given in both inches and feet. Conversion between these units will be necessary to calculate the total area correctly.
**Calculation Process:**
1. **Convert the Diameter to Feet:**
- Since 1 foot = 12 inches, convert 10 inches to feet: \(10 \text{ inches} = \frac{10}{12} \text{ feet}\).
2. **Calculate the Radius:**
- The radius \(r\) is half of the diameter: \(r = \frac{5}{12} \text{ feet}\).
3. **Calculate the Area of the Half-Circle Cross-Section:**
- The area \(A\) of a circle is \(\pi r^2\). Thus, the area of a half-circle is \(\frac{\pi r^2}{2}\).
4. **Calculate the Lateral Surface Area of the Trough:**
- Multiply the area of the half-circle by the length of the trough to find the total lateral surface area in square feet.
5. **Final Answer:**
- Calculate and fill in the blank for square feet of sheet metal needed.
\[ \_\_\_\_\_ \text{ ft}^2 \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning