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
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![**Volume Calculation for a Basketball**
**Problem Statement:**
Find the VOLUME of my basketball with a radius of 4.75 inches.
To find the volume of a sphere (which is the shape of a basketball), we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( r \) is the radius, and \( \pi \) is approximately 3.14159.
Given:
Radius \( r = 4.75 \) inches.
Let's calculate the volume step-by-step:
1. **Calculate \( r^3 \):**
\[ r^3 = (4.75)^3 = 107.171875 \text{ cubic inches} \]
2. **Substitute \( r^3 \) into the volume formula:**
\[ V = \frac{4}{3} \pi (107.171875) \]
3. **Multiply by \( \pi \):**
\[ V \approx \frac{4}{3} \times 3.14159 \times 107.171875 \]
4. **Compute the final volume:**
\[ V \approx 449.087 \text{ cubic inches} \]
Thus, the volume of the basketball is approximately 449.087 cubic inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F540f4f0d-7722-4be7-87a7-4763baf92186%2Feaa07560-31cf-4268-bbef-f3ef518a5b4f%2F9ohrrk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume Calculation for a Basketball**
**Problem Statement:**
Find the VOLUME of my basketball with a radius of 4.75 inches.
To find the volume of a sphere (which is the shape of a basketball), we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( r \) is the radius, and \( \pi \) is approximately 3.14159.
Given:
Radius \( r = 4.75 \) inches.
Let's calculate the volume step-by-step:
1. **Calculate \( r^3 \):**
\[ r^3 = (4.75)^3 = 107.171875 \text{ cubic inches} \]
2. **Substitute \( r^3 \) into the volume formula:**
\[ V = \frac{4}{3} \pi (107.171875) \]
3. **Multiply by \( \pi \):**
\[ V \approx \frac{4}{3} \times 3.14159 \times 107.171875 \]
4. **Compute the final volume:**
\[ V \approx 449.087 \text{ cubic inches} \]
Thus, the volume of the basketball is approximately 449.087 cubic inches.
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