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
![**Volume of a Sphere: Example Calculation**
**Question:**
What is the volume of a sphere with a radius of 9.2 cm, rounded to the nearest tenth of a cubic centimeter?
**Explanation and Solution:**
To find the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( V \) is the volume, \( \pi \) (pi) is approximately 3.14159, and \( r \) is the radius of the sphere.
Given:
\[ r = 9.2 \, \text{cm} \]
**Step-by-Step Calculation:**
1. First, cube the radius:
\[ r^3 = 9.2^3 = 778.688 \]
2. Next, multiply the result by \( \pi \):
\[ \pi \times 778.688 \approx 3.14159 \times 778.688 = 2447.8405 \]
3. Then, multiply by \(\frac{4}{3}\):
\[ V = \frac{4}{3} \times 2447.8405 \approx 3263.7873 \]
4. Finally, round the result to the nearest tenth:
\[ V \approx 3263.8 \, \text{cubic centimeters} \]
**Answer:**
The volume of the sphere is approximately 3263.8 cubic centimeters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71ad11dc-25a4-4aef-afaf-b0879e57e72d%2F2ddfe4f2-55be-4b2f-8f2f-f3cf32d53985%2Fofwxbh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume of a Sphere: Example Calculation**
**Question:**
What is the volume of a sphere with a radius of 9.2 cm, rounded to the nearest tenth of a cubic centimeter?
**Explanation and Solution:**
To find the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( V \) is the volume, \( \pi \) (pi) is approximately 3.14159, and \( r \) is the radius of the sphere.
Given:
\[ r = 9.2 \, \text{cm} \]
**Step-by-Step Calculation:**
1. First, cube the radius:
\[ r^3 = 9.2^3 = 778.688 \]
2. Next, multiply the result by \( \pi \):
\[ \pi \times 778.688 \approx 3.14159 \times 778.688 = 2447.8405 \]
3. Then, multiply by \(\frac{4}{3}\):
\[ V = \frac{4}{3} \times 2447.8405 \approx 3263.7873 \]
4. Finally, round the result to the nearest tenth:
\[ V \approx 3263.8 \, \text{cubic centimeters} \]
**Answer:**
The volume of the sphere is approximately 3263.8 cubic centimeters.
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