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
What is the surface area for the figure below?
For this problem, a circle is shown with a radius of 3 feet. The surface area of a sphere is calculated using the formula:
\[ \text{Surface Area} = 4\pi r^2 \]
Where \( r \) is the radius of the sphere.
**Calculation:**
\[ \text{Surface Area} = 4 \times \pi \times (3)^2 \]
\[ \text{Surface Area} = 4 \times \pi \times 9 \]
\[ \text{Surface Area} = 36\pi \]
\[ \text{Surface Area} \approx 36 \times 3.14 \]
\[ \text{Surface Area} \approx 113.1 \text{ square feet} \]
The surface area is approximately \( 113.1 \text{ square feet} \).
#### Problem 2: Volume Calculation
**Question:**
What is the volume of this sphere?
For this problem, a sphere is shown with a radius of 16 meters. The volume of a sphere is calculated using the formula:
\[ \text{Volume} = \frac{4}{3}\pi r^3 \]
Where \( r \) is the radius of the sphere.
**Calculation:**
\[ \text{Volume} = \frac{4}{3} \times \pi \times (16)^3 \]
\[ \text{Volume} = \frac{4}{3} \times \pi \times 4096 \]
\[ \text{Volume} = \frac{4}{3} \times 3.14 \times 4096 \]
\[ \text{Volume} = 4.18666 \times 4096 \]
\[ \text{Volume} \approx 17157.28 \text{ cubic meters} \]
The volume is approximately \( 17157.28 \text{ cubic meters} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e9d242-cb37-4bc8-a74f-f7cca1efbc15%2Fa65de9e0-8fc1-4086-a434-b20e2eb9efd9%2Fh5lw5f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Sphere Surface Area and Volume Calculations
#### Problem 1: Surface Area Calculation
**Question:**
What is the surface area for the figure below? Round to the nearest hundredth.
For this problem, a circle is shown with a radius of 3 feet. The surface area of a sphere is calculated using the formula:
\[ \text{Surface Area} = 4\pi r^2 \]
Where \( r \) is the radius of the sphere.
**Calculation:**
\[ \text{Surface Area} = 4 \times \pi \times (3)^2 \]
\[ \text{Surface Area} = 4 \times \pi \times 9 \]
\[ \text{Surface Area} = 36\pi \]
\[ \text{Surface Area} \approx 36 \times 3.14 \]
\[ \text{Surface Area} \approx 113.1 \text{ square feet} \]
The surface area is approximately \( 113.1 \text{ square feet} \).
#### Problem 2: Volume Calculation
**Question:**
What is the volume of this sphere?
For this problem, a sphere is shown with a radius of 16 meters. The volume of a sphere is calculated using the formula:
\[ \text{Volume} = \frac{4}{3}\pi r^3 \]
Where \( r \) is the radius of the sphere.
**Calculation:**
\[ \text{Volume} = \frac{4}{3} \times \pi \times (16)^3 \]
\[ \text{Volume} = \frac{4}{3} \times \pi \times 4096 \]
\[ \text{Volume} = \frac{4}{3} \times 3.14 \times 4096 \]
\[ \text{Volume} = 4.18666 \times 4096 \]
\[ \text{Volume} \approx 17157.28 \text{ cubic meters} \]
The volume is approximately \( 17157.28 \text{ cubic meters} \).
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