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
![### Educational Content: Solving for the Radius of a Sphere
---
#### Problem Statement:
**28. The volume of a sphere is \(972\pi\). What is the radius of the sphere?**
---
#### Explanation:
To solve for the radius of a sphere when its volume is given:
1. **Volume Formula:**
The volume \(V\) of a sphere can be found using the formula:
\[
V = \frac{4}{3} \pi r^3
\]
2. **Given Data:**
The volume of the sphere is \(972\pi\).
3. **Setting up the Equation:**
Substitute the given volume into the volume formula:
\[
972\pi = \frac{4}{3} \pi r^3
\]
4. **Solving for \(r^3\):**
Cancel out \(\pi\) from both sides:
\[
972 = \frac{4}{3} r^3
\]
To isolate \(r^3\), multiply both sides by \(\frac{3}{4}\):
\[
972 \times \frac{3}{4} = r^3
\]
Calculate:
\[
972 \times \frac{3}{4} = 729
\]
So,
\[
r^3 = 729
\]
5. **Finding the Radius \(r\):**
Take the cube root of both sides to solve for \(r\):
\[
r = \sqrt[3]{729}
\]
Calculate:
\[
r = 9
\]
6. **Answer:**
Hence, the radius of the sphere is \(9\) units.
---
#### Final Answer:
**radius = 9**
This detailed solution explains the step-by-step approach to solving for the radius of a sphere when given its volume.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc23d3db8-c01c-412d-9254-40c662c998c4%2F4d6b79df-8266-4a00-8af8-dac38d6c99bf%2F4y4tk6j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content: Solving for the Radius of a Sphere
---
#### Problem Statement:
**28. The volume of a sphere is \(972\pi\). What is the radius of the sphere?**
---
#### Explanation:
To solve for the radius of a sphere when its volume is given:
1. **Volume Formula:**
The volume \(V\) of a sphere can be found using the formula:
\[
V = \frac{4}{3} \pi r^3
\]
2. **Given Data:**
The volume of the sphere is \(972\pi\).
3. **Setting up the Equation:**
Substitute the given volume into the volume formula:
\[
972\pi = \frac{4}{3} \pi r^3
\]
4. **Solving for \(r^3\):**
Cancel out \(\pi\) from both sides:
\[
972 = \frac{4}{3} r^3
\]
To isolate \(r^3\), multiply both sides by \(\frac{3}{4}\):
\[
972 \times \frac{3}{4} = r^3
\]
Calculate:
\[
972 \times \frac{3}{4} = 729
\]
So,
\[
r^3 = 729
\]
5. **Finding the Radius \(r\):**
Take the cube root of both sides to solve for \(r\):
\[
r = \sqrt[3]{729}
\]
Calculate:
\[
r = 9
\]
6. **Answer:**
Hence, the radius of the sphere is \(9\) units.
---
#### Final Answer:
**radius = 9**
This detailed solution explains the step-by-step approach to solving for the radius of a sphere when given its volume.
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