Determine the volume and the surface area of the half-torus shown in the figure. R
Determine the volume and the surface area of the half-torus shown in the figure. R
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Title: Calculating Volume and Surface Area of a Half-Torus**
**Objective:**
Learn how to determine the volume and surface area of a half-torus using the formulas provided.
**Introduction:**
A torus is a three-dimensional shape that resembles a doughnut. It has two radii:
1. \( R \) - the distance from the center of the tube to the center of the torus.
2. \( r \) - the radius of the tube itself.
In this exercise, we will focus on a half-torus.
**Visual Representation:**
The image shows a half-torus intersecting the x-y plane. The major radius \( R \) is shown as the distance from the origin to the center of the torus, while the minor radius \( r \) is the radius of the circular cross-section of the torus.
**Formulas:**
- **Volume of the Half-Torus:**
\[
V = \pi^2 R r^2
\]
To calculate the volume, plug the known values of \( R \) and \( r \) into the formula and solve.
- **Surface Area of the Half-Torus:**
\[
A = \pi^2 R r
\]
Use the above formula for surface area to find the half-torus's surface area.
**Application:**
Fill in the blanks with the computed values for volume and surface area based on the given radii.
This exercise aims to solidify your understanding of geometric volume and surface area calculations for complex shapes like the torus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffc9e826-c865-4bea-8e1f-6dcccd31bfb0%2F88f1fec1-f02c-47c7-8255-53265672f5c6%2F8tu212k_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Volume and Surface Area of a Half-Torus**
**Objective:**
Learn how to determine the volume and surface area of a half-torus using the formulas provided.
**Introduction:**
A torus is a three-dimensional shape that resembles a doughnut. It has two radii:
1. \( R \) - the distance from the center of the tube to the center of the torus.
2. \( r \) - the radius of the tube itself.
In this exercise, we will focus on a half-torus.
**Visual Representation:**
The image shows a half-torus intersecting the x-y plane. The major radius \( R \) is shown as the distance from the origin to the center of the torus, while the minor radius \( r \) is the radius of the circular cross-section of the torus.
**Formulas:**
- **Volume of the Half-Torus:**
\[
V = \pi^2 R r^2
\]
To calculate the volume, plug the known values of \( R \) and \( r \) into the formula and solve.
- **Surface Area of the Half-Torus:**
\[
A = \pi^2 R r
\]
Use the above formula for surface area to find the half-torus's surface area.
**Application:**
Fill in the blanks with the computed values for volume and surface area based on the given radii.
This exercise aims to solidify your understanding of geometric volume and surface area calculations for complex shapes like the torus.
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 1 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning


Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON

Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning

Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education


Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning