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
![### Problem Statement
A table tennis ball has a diameter of 40 mm. What is the value of the surface area of the table tennis ball, in square millimeters?
### Solution Approach
To find the surface area of the table tennis ball, we can use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
- \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159.
Given:
- The diameter of the table tennis ball is 40 mm.
Since the radius \( r \) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{40 \text{ mm}}{2} = 20 \text{ mm} \]
Now, substitute \( r = 20 \text{ mm} \) into the surface area formula:
\[ \text{Surface Area} = 4\pi (20 \text{ mm})^2 \]
First, calculate \( (20 \text{ mm})^2 \):
\[ (20 \text{ mm})^2 = 400 \text{ mm}^2 \]
Then, multiply by \( 4\pi \):
\[ \text{Surface Area} = 4\pi \times 400 \text{ mm}^2 \]
\[ \text{Surface Area} = 1600\pi \text{ mm}^2 \]
Finally, approximate using \( \pi \approx 3.14159 \):
\[ \text{Surface Area} \approx 1600 \times 3.14159 \text{ mm}^2 \]
\[ \text{Surface Area} \approx 5026.56 \text{ mm}^2 \]
Therefore, the surface area of the table tennis ball is approximately \( 5026.56 \text{ mm}^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a5f7bb8-38e7-4a5a-bfc7-c8f4b1290a9a%2Fa8df95d2-4444-45c1-ad6f-53c3fd846c48%2F8a4p5cq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A table tennis ball has a diameter of 40 mm. What is the value of the surface area of the table tennis ball, in square millimeters?
### Solution Approach
To find the surface area of the table tennis ball, we can use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
- \( \pi \) (pi) is a mathematical constant approximately equal to 3.14159.
Given:
- The diameter of the table tennis ball is 40 mm.
Since the radius \( r \) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{40 \text{ mm}}{2} = 20 \text{ mm} \]
Now, substitute \( r = 20 \text{ mm} \) into the surface area formula:
\[ \text{Surface Area} = 4\pi (20 \text{ mm})^2 \]
First, calculate \( (20 \text{ mm})^2 \):
\[ (20 \text{ mm})^2 = 400 \text{ mm}^2 \]
Then, multiply by \( 4\pi \):
\[ \text{Surface Area} = 4\pi \times 400 \text{ mm}^2 \]
\[ \text{Surface Area} = 1600\pi \text{ mm}^2 \]
Finally, approximate using \( \pi \approx 3.14159 \):
\[ \text{Surface Area} \approx 1600 \times 3.14159 \text{ mm}^2 \]
\[ \text{Surface Area} \approx 5026.56 \text{ mm}^2 \]
Therefore, the surface area of the table tennis ball is approximately \( 5026.56 \text{ mm}^2 \).
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