XFind the volume of the composite figure. Round to the nearest hundredth. 4 in. 2 in. 5 in. 77.6 This form was created inside of Hillsborough Township Public Schools. Google Forms M
XFind the volume of the composite figure. Round to the nearest hundredth. 4 in. 2 in. 5 in. 77.6 This form was created inside of Hillsborough Township Public Schools. Google Forms M
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
find the volume of the composite figure
![**Find the Volume of the Composite Figure**
**Objective:**
Calculate the volume of the composite figure, rounding the result to the nearest hundredth.
**Description:**
The composite figure consists of two main parts: a cone on top of a cylinder. Below are the given dimensions:
1. **Cone:**
- Radius (r): 2 inches.
- Height (h): 4 inches.
2. **Cylinder:**
- Radius (r): 2 inches.
- Height (h): 5 inches.
**Calculations:**
1. **Volume of the Cone:**
The formula to calculate the volume of a cone is:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the given values:
\[
V = \frac{1}{3} \pi (2)^2 (4) = \frac{1}{3} \pi (4)(4) = \frac{1}{3} \pi (16) = \frac{16}{3} \pi \approx 16.76 \, \text{in}^3
\]
2. **Volume of the Cylinder:**
The formula to calculate the volume of a cylinder is:
\[
V = \pi r^2 h
\]
Substituting the given values:
\[
V = \pi (2)^2 (5) = \pi (4)(5) = 20 \pi \approx 62.83 \, \text{in}^3
\]
**Total Volume of Composite Figure:**
\[
V_{\text{total}} = V_{\text{cone}} + V_{\text{cylinder}} = 16.76 \, \text{in}^3 + 62.83 \, \text{in}^3 \approx 79.59 \, \text{in}^3
\]
Therefore, the volume of the composite figure is approximately **79.59 cubic inches** when rounded to the nearest hundredth.
**Diagram Explanation:**
The diagram supports these calculations by visually representing the composite figure. The cone is positioned directly atop the cylinder, sharing the same radius of 2 inches. The height of the cone is labeled as 4 inches, and the height of the cylinder is labeled as 5 inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2Fdd556aba-f349-4c02-8b65-8ea861152809%2F1ejyu1l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Volume of the Composite Figure**
**Objective:**
Calculate the volume of the composite figure, rounding the result to the nearest hundredth.
**Description:**
The composite figure consists of two main parts: a cone on top of a cylinder. Below are the given dimensions:
1. **Cone:**
- Radius (r): 2 inches.
- Height (h): 4 inches.
2. **Cylinder:**
- Radius (r): 2 inches.
- Height (h): 5 inches.
**Calculations:**
1. **Volume of the Cone:**
The formula to calculate the volume of a cone is:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the given values:
\[
V = \frac{1}{3} \pi (2)^2 (4) = \frac{1}{3} \pi (4)(4) = \frac{1}{3} \pi (16) = \frac{16}{3} \pi \approx 16.76 \, \text{in}^3
\]
2. **Volume of the Cylinder:**
The formula to calculate the volume of a cylinder is:
\[
V = \pi r^2 h
\]
Substituting the given values:
\[
V = \pi (2)^2 (5) = \pi (4)(5) = 20 \pi \approx 62.83 \, \text{in}^3
\]
**Total Volume of Composite Figure:**
\[
V_{\text{total}} = V_{\text{cone}} + V_{\text{cylinder}} = 16.76 \, \text{in}^3 + 62.83 \, \text{in}^3 \approx 79.59 \, \text{in}^3
\]
Therefore, the volume of the composite figure is approximately **79.59 cubic inches** when rounded to the nearest hundredth.
**Diagram Explanation:**
The diagram supports these calculations by visually representing the composite figure. The cone is positioned directly atop the cylinder, sharing the same radius of 2 inches. The height of the cone is labeled as 4 inches, and the height of the cylinder is labeled as 5 inches.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 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