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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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**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:** \[ SA = \, __________ \,\text{ square feet} \]
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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