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
![**Question 21: Sphere Volume Calculation**
*Problem Statement:*
Find the approximate volume of a sphere with radius \( r = 2.7 \, cm \).
*Explanation:*
To calculate the volume of a sphere, the formula to use is:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) represents the volume.
- \( r \) is the radius of the sphere.
- \(\pi \) (Pi) is a mathematical constant approximately equal to 3.14159.
For a sphere with a radius (\( r \)) of 2.7 cm, follow these steps:
1. Cube the radius:
\[ r^3 = (2.7 \, cm)^3 \]
2. Multiply the cubed radius by \(\pi \):
\[ \pi r^3 \approx 3.14159 \times (2.7)^3 \]
3. Multiply by \(\frac{4}{3} \):
\[ V = \frac{4}{3} \pi (2.7)^3 \]
*Solution:*
1. Calculate \( r^3 \):
\[ (2.7)^3 = 19.683 \, cm^3 \]
2. Multiply by \(\pi \):
\[ 3.14159 \times 19.683 \approx 61.880 \]
3. Finally, apply \(\frac{4}{3} \):
\[ V = \frac{4}{3} \times 61.880 \approx 82.506 \, cm^3 \]
Hence, the approximate volume of the sphere is 82.506 cubic centimeters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55a87db1-34dd-4361-bb49-0fd4dde658a5%2F8a30b0b1-b0d5-4288-a817-f208b582c0d7%2F4aegz9.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 21: Sphere Volume Calculation**
*Problem Statement:*
Find the approximate volume of a sphere with radius \( r = 2.7 \, cm \).
*Explanation:*
To calculate the volume of a sphere, the formula to use is:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) represents the volume.
- \( r \) is the radius of the sphere.
- \(\pi \) (Pi) is a mathematical constant approximately equal to 3.14159.
For a sphere with a radius (\( r \)) of 2.7 cm, follow these steps:
1. Cube the radius:
\[ r^3 = (2.7 \, cm)^3 \]
2. Multiply the cubed radius by \(\pi \):
\[ \pi r^3 \approx 3.14159 \times (2.7)^3 \]
3. Multiply by \(\frac{4}{3} \):
\[ V = \frac{4}{3} \pi (2.7)^3 \]
*Solution:*
1. Calculate \( r^3 \):
\[ (2.7)^3 = 19.683 \, cm^3 \]
2. Multiply by \(\pi \):
\[ 3.14159 \times 19.683 \approx 61.880 \]
3. Finally, apply \(\frac{4}{3} \):
\[ V = \frac{4}{3} \times 61.880 \approx 82.506 \, cm^3 \]
Hence, the approximate volume of the sphere is 82.506 cubic centimeters.
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