A volleyball is inflated until it has a diameter of 12 inches. How many cubic inches of air does it contain to the nearest whole cubic inch? 1) 904 2) 905 3) 7238 4) 7239
A volleyball is inflated until it has a diameter of 12 inches. How many cubic inches of air does it contain to the nearest whole cubic inch? 1) 904 2) 905 3) 7238 4) 7239
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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Question
![**Example Problem for Volume Calculation**
**Problem:**
A volleyball is inflated until it has a diameter of 12 inches. How many cubic inches of air does it contain to the nearest whole cubic inch?
**Options:**
1) 904
2) 905
3) 7238
4) 7239
**Solution Explanation:**
To find the volume of the volleyball, we need to calculate the volume of a sphere since the volleyball approximates a spherical shape.
The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius of the sphere.
Given that the diameter of the volleyball is 12 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ inches} \]
Now, substituting \( r \) into the formula:
\[ V = \frac{4}{3} \pi (6)^3 \]
\[ V = \frac{4}{3} \pi (216) \]
\[ V = \frac{864}{3} \pi \]
\[ V = 288 \pi \]
Using the approximation \( \pi \approx 3.14159 \):
\[ V \approx 288 \times 3.14159 \]
\[ V \approx 904.77868 \]
To the nearest whole cubic inch, the volume is approximately:
\[ \boxed{905} \]
Therefore, the correct option is (2) 905.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff93478-fd93-4e87-bf04-0fc4e955b42c%2F03645e07-da01-4c86-b92f-81eef9f18e8b%2F94ce6ji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem for Volume Calculation**
**Problem:**
A volleyball is inflated until it has a diameter of 12 inches. How many cubic inches of air does it contain to the nearest whole cubic inch?
**Options:**
1) 904
2) 905
3) 7238
4) 7239
**Solution Explanation:**
To find the volume of the volleyball, we need to calculate the volume of a sphere since the volleyball approximates a spherical shape.
The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius of the sphere.
Given that the diameter of the volleyball is 12 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{12}{2} = 6 \text{ inches} \]
Now, substituting \( r \) into the formula:
\[ V = \frac{4}{3} \pi (6)^3 \]
\[ V = \frac{4}{3} \pi (216) \]
\[ V = \frac{864}{3} \pi \]
\[ V = 288 \pi \]
Using the approximation \( \pi \approx 3.14159 \):
\[ V \approx 288 \times 3.14159 \]
\[ V \approx 904.77868 \]
To the nearest whole cubic inch, the volume is approximately:
\[ \boxed{905} \]
Therefore, the correct option is (2) 905.
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