ssessments/416878/ FILE UPLOAD Question 7 What is the surface area and volume of the sphere shown below? 18 cm I HINT: SA = 4T² V = πr³ Your response should show all necessary calculations and diagrams. Photos
ssessments/416878/ FILE UPLOAD Question 7 What is the surface area and volume of the sphere shown below? 18 cm I HINT: SA = 4T² V = πr³ Your response should show all necessary calculations and diagrams. Photos
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 and volume of the sphere shown below?
![**Topic: Surface Area and Volume Calculation of a Sphere**
**Question 7:**
What is the surface area and volume of the sphere shown below?
*Diagram Description:*
The diagram shows a sphere with a diameter of 18 cm. The diameter is indicated by a horizontal dashed line passing through the center of the sphere.
**Hint:**
- Surface Area (SA) of a sphere is given by the formula: \( SA = 4\pi r^2 \)
- Volume (V) of a sphere is given by the formula: \(\displaystyle V = \frac{4}{3}\pi r^3 \)
Here, \( r \) is the radius of the sphere. Since the diameter of the sphere is 18 cm, the radius \( r \) is half of the diameter.
That is, \( r = \frac{18 \text{ cm}}{2} = 9 \text{ cm} \).
To find the surface area and volume, substitute \( r = 9 \text{ cm} \) into the formulas.
- **Surface Area Calculation:**
\[
SA = 4\pi r^2
\]
\[
SA = 4\pi (9 \text{ cm})^2
\]
\[
SA = 4\pi (81 \text{ cm}^2)
\]
\[
SA = 324\pi \text{ cm}^2
\]
- **Volume Calculation:**
\[
V = \frac{4}{3}\pi r^3
\]
\[
V = \frac{4}{3}\pi (9 \text{ cm})^3
\]
\[
V = \frac{4}{3}\pi (729 \text{ cm}^3)
\]
\[
V = \frac{2916\pi}{3} \text{ cm}^3
\]
\[
V = 972\pi \text{ cm}^3
\]
**Your response should show all necessary calculations and diagrams.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2341670b-b058-481d-a7e7-89b8beb6d704%2F1d592615-0551-4d0f-884f-81ceb29674d3%2F70tcyx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Surface Area and Volume Calculation of a Sphere**
**Question 7:**
What is the surface area and volume of the sphere shown below?
*Diagram Description:*
The diagram shows a sphere with a diameter of 18 cm. The diameter is indicated by a horizontal dashed line passing through the center of the sphere.
**Hint:**
- Surface Area (SA) of a sphere is given by the formula: \( SA = 4\pi r^2 \)
- Volume (V) of a sphere is given by the formula: \(\displaystyle V = \frac{4}{3}\pi r^3 \)
Here, \( r \) is the radius of the sphere. Since the diameter of the sphere is 18 cm, the radius \( r \) is half of the diameter.
That is, \( r = \frac{18 \text{ cm}}{2} = 9 \text{ cm} \).
To find the surface area and volume, substitute \( r = 9 \text{ cm} \) into the formulas.
- **Surface Area Calculation:**
\[
SA = 4\pi r^2
\]
\[
SA = 4\pi (9 \text{ cm})^2
\]
\[
SA = 4\pi (81 \text{ cm}^2)
\]
\[
SA = 324\pi \text{ cm}^2
\]
- **Volume Calculation:**
\[
V = \frac{4}{3}\pi r^3
\]
\[
V = \frac{4}{3}\pi (9 \text{ cm})^3
\]
\[
V = \frac{4}{3}\pi (729 \text{ cm}^3)
\]
\[
V = \frac{2916\pi}{3} \text{ cm}^3
\]
\[
V = 972\pi \text{ cm}^3
\]
**Your response should show all necessary calculations and diagrams.**
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