Homework Help is Here – Start Your Trial Now!
Math
Geometry
How many square feet of sheet metal are needed to form the trough shown in the figure below? 10.0 in. 12 ft Half circle

How many square feet of sheet metal are needed to form the trough shown in the figure below? 10.0 in. 12 ft Half circle

Elementary Geometry For College Students, 7e
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
See similar textbooks
icon
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. \[ \_\_\_\_\_ \text{ ft}^2 \]
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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer