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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![**Problem 6: Calculating the Surface Area of a Sphere**
**Description:**
The given diagram represents a sphere. One of the dashed lines labeled "8.6 ft" is indicated as the diameter of the sphere.
**Diagram Explanation:**
- A dashed vertical line through the sphere represents the diameter.
- A horizontal dashed line also indicates the diameter of the sphere.
- Both lines intersect at the center of the sphere and are labeled as 8.6 feet in length.
**Objective:**
Calculate the surface area (SA) of the sphere.
**Formula for Calculating Surface Area of a Sphere:**
To find the surface area of a sphere, use the formula:
\[ SA = 4\pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
Since the diameter (d) of the sphere is given as 8.6 ft, we can find the radius (r) by:
\[ r = \frac{d}{2} = \frac{8.6}{2} = 4.3 \text{ ft} \]
Now, Substitute \( r = 4.3 \text{ ft} \) into the formula to determine the surface area:
\[ SA = 4\pi (4.3)^2 \]
**Calculation:**
\[ SA = 4\pi (18.49) \]
\[ SA = 73.96\pi \]
Hence, the surface area \( SA \), when calculated, will be expressed in square feet.
**Result:**
\[ SA = \, __________ \,\text{ square feet} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a5f7bb8-38e7-4a5a-bfc7-c8f4b1290a9a%2F77dc5f90-0cfa-455b-b658-22d53600e537%2Fsaapuhh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 6: Calculating the Surface Area of a Sphere**
**Description:**
The given diagram represents a sphere. One of the dashed lines labeled "8.6 ft" is indicated as the diameter of the sphere.
**Diagram Explanation:**
- A dashed vertical line through the sphere represents the diameter.
- A horizontal dashed line also indicates the diameter of the sphere.
- Both lines intersect at the center of the sphere and are labeled as 8.6 feet in length.
**Objective:**
Calculate the surface area (SA) of the sphere.
**Formula for Calculating Surface Area of a Sphere:**
To find the surface area of a sphere, use the formula:
\[ SA = 4\pi r^2 \]
Where:
- \( r \) is the radius of the sphere.
Since the diameter (d) of the sphere is given as 8.6 ft, we can find the radius (r) by:
\[ r = \frac{d}{2} = \frac{8.6}{2} = 4.3 \text{ ft} \]
Now, Substitute \( r = 4.3 \text{ ft} \) into the formula to determine the surface area:
\[ SA = 4\pi (4.3)^2 \]
**Calculation:**
\[ SA = 4\pi (18.49) \]
\[ SA = 73.96\pi \]
Hence, the surface area \( SA \), when calculated, will be expressed in square feet.
**Result:**
\[ SA = \, __________ \,\text{ square feet} \]
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