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22) A sphere with r = 4 cm radius (a sphere) A) 67.0 cm2 B) 200.8 cm2 C) 267.9 cm2 D) 50.2 cm2

22) A sphere with r = 4 cm radius (a sphere) A) 67.0 cm2 B) 200.8 cm2 C) 267.9 cm2 D) 50.2 cm2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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How would I go about calculating the surface area?

### Question 22: Surface Area of a Sphere #### Problem Statement A sphere with a radius (r) of 4 cm is given. Calculate the surface area of the sphere. #### Diagram The diagram provided shows a sphere with a labeled radius. The radius is indicated as a line extending from the center of the sphere to its surface. The sphere is simply labeled as "a sphere." #### Options - A) 67.0 cm² - B) 200.8 cm² - C) 267.9 cm² - D) 50.2 cm² #### Explanation To solve this problem, you will use the formula for the surface area of a sphere: \[ \text{Surface Area} = 4 \pi r^2 \] Given: - Radius \( r = 4 \, \text{cm} \) - \(\pi \approx 3.14\) Step-by-Step Solution: 1. Calculate \( r^2 \): \[ r^2 = 4^2 = 16 \, \text{cm}^2 \] 2. Multiply by \(\pi\): \[ 4 \pi r^2 = 4 \times 3.14 \times 16 \] 3. Simplify the multiplication: \[ 4 \times 3.14 = 12.56 \] \[ 12.56 \times 16 = 200.96 \, \text{cm}^2 \] The closest option to 200.96 cm² is: - **B) 200.8 cm²** Thus, the answer is **B) 200.8 cm²**.
Transcribed Image Text:### Question 22: Surface Area of a Sphere #### Problem Statement A sphere with a radius (r) of 4 cm is given. Calculate the surface area of the sphere. #### Diagram The diagram provided shows a sphere with a labeled radius. The radius is indicated as a line extending from the center of the sphere to its surface. The sphere is simply labeled as "a sphere." #### Options - A) 67.0 cm² - B) 200.8 cm² - C) 267.9 cm² - D) 50.2 cm² #### Explanation To solve this problem, you will use the formula for the surface area of a sphere: \[ \text{Surface Area} = 4 \pi r^2 \] Given: - Radius \( r = 4 \, \text{cm} \) - \(\pi \approx 3.14\) Step-by-Step Solution: 1. Calculate \( r^2 \): \[ r^2 = 4^2 = 16 \, \text{cm}^2 \] 2. Multiply by \(\pi\): \[ 4 \pi r^2 = 4 \times 3.14 \times 16 \] 3. Simplify the multiplication: \[ 4 \times 3.14 = 12.56 \] \[ 12.56 \times 16 = 200.96 \, \text{cm}^2 \] The closest option to 200.96 cm² is: - **B) 200.8 cm²** Thus, the answer is **B) 200.8 cm²**.
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