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
![**Problem Statement:**
The diameter of a sphere is 18 m. Find its surface area.
**Diagram Description:**
The image includes a diagram of a sphere with a line passing through its center, labeled with the diameter of 18 m.
**Solution Options:**
- 3052.08 m²
- 4069.44 m²
- 1017.36 m²
- 508.68 m²
**Solution:**
To find the surface area of the sphere, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Given:
- Diameter \( d = 18 \) m
- Radius \( r = \frac{d}{2} = \frac{18}{2} = 9 \) m
Substitute \( r \) into the surface area formula:
\[ \text{Surface Area} = 4\pi (9)^2 \]
\[ \text{Surface Area} = 4\pi \times 81 \]
\[ \text{Surface Area} = 324\pi \]
Using \( \pi \approx 3.14159 \):
\[ \text{Surface Area} \approx 324 \times 3.14159 = 1017.36 \text{ m}^2 \]
Thus, the correct answer is:
- 1017.36 m²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b5161d0-8c1c-4aef-9d6c-2e647d1b4222%2Fb9192c7b-cbab-4f30-ac47-ca7e02ff55ee%2F3ama5bc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The diameter of a sphere is 18 m. Find its surface area.
**Diagram Description:**
The image includes a diagram of a sphere with a line passing through its center, labeled with the diameter of 18 m.
**Solution Options:**
- 3052.08 m²
- 4069.44 m²
- 1017.36 m²
- 508.68 m²
**Solution:**
To find the surface area of the sphere, we will use the formula for the surface area of a sphere:
\[ \text{Surface Area} = 4\pi r^2 \]
Given:
- Diameter \( d = 18 \) m
- Radius \( r = \frac{d}{2} = \frac{18}{2} = 9 \) m
Substitute \( r \) into the surface area formula:
\[ \text{Surface Area} = 4\pi (9)^2 \]
\[ \text{Surface Area} = 4\pi \times 81 \]
\[ \text{Surface Area} = 324\pi \]
Using \( \pi \approx 3.14159 \):
\[ \text{Surface Area} \approx 324 \times 3.14159 = 1017.36 \text{ m}^2 \]
Thus, the correct answer is:
- 1017.36 m²
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