Let's model R2-D2's body with a cylinder of height 3 feet and radius 0.75 feet and head with a semi-sphere of radius 0.75 feet. What is the total volume of R2-D2's body and head? *
Let's model R2-D2's body with a cylinder of height 3 feet and radius 0.75 feet and head with a semi-sphere of radius 0.75 feet. What is the total volume of R2-D2's body and head? *
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
Let’s model R2-D2’s body with a cylinder of height 3 feet and radius 0.75 feet and head with a semi-sphere of radius 0.75 feet. What is the total volume of R2-D2’s body and head?
![**Modeling R2-D2's Body and Head: Calculating Volume**
Let's model R2-D2's body with a cylinder of height 3 feet and radius 0.75 feet and head with a semi-sphere of radius 0.75 feet. What is the total volume of R2-D2's body and head?
**Diagram Explanation:**
- The diagram shows a cylinder with a semi-sphere on top.
- The cylinder has a radius (r) of 0.75 feet and a height (h) of 3 feet.
- The semi-sphere, which represents R2-D2's head, also has a radius (r) of 0.75 feet.
### Calculations:
1. **Volume of the Cylinder:**
The formula for the volume of a cylinder is \(V = \pi r^2 h\).
Substituting the given values:
\[
V_{\text{cylinder}} = \pi \times (0.75)^2 \times 3
\]
2. **Volume of the Semi-Sphere:**
The formula for the volume of a sphere is \(V = \frac{4}{3} \pi r^3\), and for a semi-sphere it is \(\frac{1}{2}\) of that.
Substituting the given values:
\[
V_{\text{semi-sphere}} = \frac{1}{2} \times \frac{4}{3} \pi \times (0.75)^3
\]
3. **Total Volume:**
Sum the volumes of the cylinder and the semi-sphere.
\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{semi-sphere}}
\]
By calculating the above formulas, we get the total volume of R2-D2’s body and head.
These calculations allow us to model R2-D2’s volume as a combination of simple geometric shapes, which can be useful in various educational and engineering contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feceeade0-6901-495b-831b-4977811a6c19%2F15214bd8-70ee-49ad-b80a-2015380572ee%2Fgexjda9_processed.png&w=3840&q=75)
Transcribed Image Text:**Modeling R2-D2's Body and Head: Calculating Volume**
Let's model R2-D2's body with a cylinder of height 3 feet and radius 0.75 feet and head with a semi-sphere of radius 0.75 feet. What is the total volume of R2-D2's body and head?
**Diagram Explanation:**
- The diagram shows a cylinder with a semi-sphere on top.
- The cylinder has a radius (r) of 0.75 feet and a height (h) of 3 feet.
- The semi-sphere, which represents R2-D2's head, also has a radius (r) of 0.75 feet.
### Calculations:
1. **Volume of the Cylinder:**
The formula for the volume of a cylinder is \(V = \pi r^2 h\).
Substituting the given values:
\[
V_{\text{cylinder}} = \pi \times (0.75)^2 \times 3
\]
2. **Volume of the Semi-Sphere:**
The formula for the volume of a sphere is \(V = \frac{4}{3} \pi r^3\), and for a semi-sphere it is \(\frac{1}{2}\) of that.
Substituting the given values:
\[
V_{\text{semi-sphere}} = \frac{1}{2} \times \frac{4}{3} \pi \times (0.75)^3
\]
3. **Total Volume:**
Sum the volumes of the cylinder and the semi-sphere.
\[
V_{\text{total}} = V_{\text{cylinder}} + V_{\text{semi-sphere}}
\]
By calculating the above formulas, we get the total volume of R2-D2’s body and head.
These calculations allow us to model R2-D2’s volume as a combination of simple geometric shapes, which can be useful in various educational and engineering contexts.
Transcribed Image Text:For a sphere with radius, \( r \), its volume is \( \frac{4}{3} \pi r^3 \).
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 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.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