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
![### Sphere Volume Calculation
#### Problem:
Find the volume of the sphere.
#### Description:
The image depicts a sphere with a diameter of 8 inches.
#### Diagram Explanation:
- The sphere is a perfectly round geometrical object in three-dimensional space.
- It has a label "8 in" which denotes the diameter of the sphere.
#### Solution:
To find the volume of a sphere, use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( V \) is the volume and \( r \) is the radius of the sphere.
Given:
- Diameter \( d = 8 \) inches
- Radius \( r = \frac{d}{2} = \frac{8}{2} = 4 \) inches
Now, apply the radius to the formula:
\[ V = \frac{4}{3} \pi (4)^3 \]
\[ V = \frac{4}{3} \pi (64) \]
\[ V = \frac{256}{3} \pi \]
Thus,
\[ V \approx \frac{256}{3} \times 3.14 \]
\[ V \approx 268.08 \; \text{cubic inches} \]
Therefore, the volume of the sphere is approximately 268.08 cubic inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d6f4483-a5c4-47f8-8074-8ffd9480bb0e%2F6f823fae-4c2d-4d75-b61b-c6631dc9641f%2Fr2kwu9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sphere Volume Calculation
#### Problem:
Find the volume of the sphere.
#### Description:
The image depicts a sphere with a diameter of 8 inches.
#### Diagram Explanation:
- The sphere is a perfectly round geometrical object in three-dimensional space.
- It has a label "8 in" which denotes the diameter of the sphere.
#### Solution:
To find the volume of a sphere, use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( V \) is the volume and \( r \) is the radius of the sphere.
Given:
- Diameter \( d = 8 \) inches
- Radius \( r = \frac{d}{2} = \frac{8}{2} = 4 \) inches
Now, apply the radius to the formula:
\[ V = \frac{4}{3} \pi (4)^3 \]
\[ V = \frac{4}{3} \pi (64) \]
\[ V = \frac{256}{3} \pi \]
Thus,
\[ V \approx \frac{256}{3} \times 3.14 \]
\[ V \approx 268.08 \; \text{cubic inches} \]
Therefore, the volume of the sphere is approximately 268.08 cubic inches.
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