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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
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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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.**
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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