Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision How many square feet of sheet metal are needed to form the trough shown in the figure below? 10.0 in. 19 ft Half circle ft2
Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision How many square feet of sheet metal are needed to form the trough shown in the figure below? 10.0 in. 19 ft Half circle ft2
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![**Title: Calculating Sheet Metal Requirements for a Half-Cylinder Trough**
**Instructions:**
Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision.
**Problem Statement:**
How many square feet of sheet metal are needed to form the trough shown in the figure below?
**Diagram Description:**
The diagram depicts a three-dimensional trough with the shape of a half-cylinder. It includes the following measurements:
- The diameter of the half-cylinder is labeled as 10.0 inches.
- The length of the cylindrical trough is 19 feet.
The label "Half circle" identifies the semicircular cross-section of the trough.
**Calculation Area:**
\[ \text{Area in square feet} = \_ \_ \_ \_ \_ \]
**Steps for Calculation:**
1. **Convert Measurements:**
- Convert the diameter from inches to feet: 10.0 inches = \( \frac{10.0}{12} \) feet.
2. **Calculate the Radius:**
- Radius \( r \) = \( \frac{\text{Diameter}}{2} \).
3. **Surface Area of the Half-Cylinder:**
- Use the formula for the lateral surface area of a cylinder:
\[
\text{Area} = \pi \times \text{radius} \times \text{length}
\]
- Since it is a half-cylinder, divide the lateral area by 2.
4. **Add the Area of the Circular Ends:**
- Calculate the area of one circular end of the cylinder and add it to the lateral area. For a half-cylinder, this equals the area of one full circle (since the opposite open sides contribute half-circle areas each):
\[
\text{Area of one end} = \pi \times (\text{radius})^2
\]
5. **Total Surface Area:**
- Sum the lateral surface area and the area of the circular end to find the total required sheet metal area in square feet.
**Note:**
Ensure unit consistency and precise calculations to answer accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F355817fc-4afc-456c-bc56-6563b808926d%2F5fe50db7-3aff-4567-ada7-fefee6328893%2Ft9nbri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Sheet Metal Requirements for a Half-Cylinder Trough**
**Instructions:**
Use the rules for working with measurements to give your answer to the appropriate accuracy and/or precision.
**Problem Statement:**
How many square feet of sheet metal are needed to form the trough shown in the figure below?
**Diagram Description:**
The diagram depicts a three-dimensional trough with the shape of a half-cylinder. It includes the following measurements:
- The diameter of the half-cylinder is labeled as 10.0 inches.
- The length of the cylindrical trough is 19 feet.
The label "Half circle" identifies the semicircular cross-section of the trough.
**Calculation Area:**
\[ \text{Area in square feet} = \_ \_ \_ \_ \_ \]
**Steps for Calculation:**
1. **Convert Measurements:**
- Convert the diameter from inches to feet: 10.0 inches = \( \frac{10.0}{12} \) feet.
2. **Calculate the Radius:**
- Radius \( r \) = \( \frac{\text{Diameter}}{2} \).
3. **Surface Area of the Half-Cylinder:**
- Use the formula for the lateral surface area of a cylinder:
\[
\text{Area} = \pi \times \text{radius} \times \text{length}
\]
- Since it is a half-cylinder, divide the lateral area by 2.
4. **Add the Area of the Circular Ends:**
- Calculate the area of one circular end of the cylinder and add it to the lateral area. For a half-cylinder, this equals the area of one full circle (since the opposite open sides contribute half-circle areas each):
\[
\text{Area of one end} = \pi \times (\text{radius})^2
\]
5. **Total Surface Area:**
- Sum the lateral surface area and the area of the circular end to find the total required sheet metal area in square feet.
**Note:**
Ensure unit consistency and precise calculations to answer accurately.
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