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 27: Calculating the Surface Area of a Sphere
#### Question
Find the surface area of a sphere with a circumference of 50 feet. Round to the nearest tenth.
#### Instructions
1. Fill in your detailed work in the 'Work' section provided.
2. Complete the calculation to find the surface area.
3. Report your final answer in the 'Surface Area' box.
#### Work
*Note:* Use the formula for the circumference of a sphere to find the radius, and then use the radius to find the surface area of the sphere. Here are the steps you can follow:
- Circumference of a sphere formula: \( C = 2\pi r \)
- Surface area of a sphere formula: \( A = 4\pi r^2 \)
Given:
- Circumference (C) = 50 feet
Step-by-step solution:
1. Solve for radius (r):
\[
C = 2\pi r
\]
\[
50 = 2\pi r
\]
\[
r = \frac{50}{2\pi}
\]
\[
r \approx \frac{50}{6.2832}
\]
\[
r \approx 7.96 \, \text{feet}
\]
2. Now use the radius to find the surface area (A):
\[
A = 4\pi r^2
\]
\[
A = 4\pi (7.96)^2
\]
\[
A \approx 4 \times 3.1416 \times 63.4
\]
\[
A \approx 796.2 \, \text{square feet}
\]
#### Surface Area
\[\boxed{796.2 \, \text{ft}^2}\]
Feel free to plug in the radius and perform the calculation again for precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dffb718-983b-46b0-ad4c-cd5e69abfc5e%2F5e671f92-40aa-4ee9-b1ec-1858d3a45762%2F7acvnvu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 27: Calculating the Surface Area of a Sphere
#### Question
Find the surface area of a sphere with a circumference of 50 feet. Round to the nearest tenth.
#### Instructions
1. Fill in your detailed work in the 'Work' section provided.
2. Complete the calculation to find the surface area.
3. Report your final answer in the 'Surface Area' box.
#### Work
*Note:* Use the formula for the circumference of a sphere to find the radius, and then use the radius to find the surface area of the sphere. Here are the steps you can follow:
- Circumference of a sphere formula: \( C = 2\pi r \)
- Surface area of a sphere formula: \( A = 4\pi r^2 \)
Given:
- Circumference (C) = 50 feet
Step-by-step solution:
1. Solve for radius (r):
\[
C = 2\pi r
\]
\[
50 = 2\pi r
\]
\[
r = \frac{50}{2\pi}
\]
\[
r \approx \frac{50}{6.2832}
\]
\[
r \approx 7.96 \, \text{feet}
\]
2. Now use the radius to find the surface area (A):
\[
A = 4\pi r^2
\]
\[
A = 4\pi (7.96)^2
\]
\[
A \approx 4 \times 3.1416 \times 63.4
\]
\[
A \approx 796.2 \, \text{square feet}
\]
#### Surface Area
\[\boxed{796.2 \, \text{ft}^2}\]
Feel free to plug in the radius and perform the calculation again for precision.
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