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What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit. 6 units? 24 units? 98 units? 136 units2 0000

What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit. 6 units? 24 units? 98 units? 136 units2 0000

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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**Problem Statement:** What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit. **Answer Choices:** - ☐ 6 units² - ☐ 24 units² - ☐ 98 units² - ☐ 136 units² **Solution Explanation:** First, we need to determine the radius of the circle using the given circumference. The formula for the circumference (C) of a circle is: \[ C = 2\pi r \] Given \( C = 10 \) units, \[ 10 = 2\pi r \] \[ r = \frac{10}{2\pi} \] \[ r \approx \frac{10}{6.2832} \] \[ r \approx 1.59 \] units Next, we calculate the area (A) of the circle using the radius. The formula for the area of a circle is: \[ A = \pi r^2 \] \[ A \approx \pi (1.59)^2 \] \[ A \approx 3.1416 \times 2.5281 \] \[ A \approx 7.95 \] square units To find 75% of this area, \[ 75\% \text{ of } 7.95 = 0.75 \times 7.95 \] \[ \approx 5.96 \] square units Rounded to the nearest square unit, it is: \[ 6 \text{ units}^2 \] Thus, the answer is: - ☑ 6 units² - ☐ 24 units² - ☐ 98 units² - ☐ 136 units²
Transcribed Image Text:**Problem Statement:** What is 75% of the area of a circle with a circumference of 10 units? Round the solution to the nearest square unit. **Answer Choices:** - ☐ 6 units² - ☐ 24 units² - ☐ 98 units² - ☐ 136 units² **Solution Explanation:** First, we need to determine the radius of the circle using the given circumference. The formula for the circumference (C) of a circle is: \[ C = 2\pi r \] Given \( C = 10 \) units, \[ 10 = 2\pi r \] \[ r = \frac{10}{2\pi} \] \[ r \approx \frac{10}{6.2832} \] \[ r \approx 1.59 \] units Next, we calculate the area (A) of the circle using the radius. The formula for the area of a circle is: \[ A = \pi r^2 \] \[ A \approx \pi (1.59)^2 \] \[ A \approx 3.1416 \times 2.5281 \] \[ A \approx 7.95 \] square units To find 75% of this area, \[ 75\% \text{ of } 7.95 = 0.75 \times 7.95 \] \[ \approx 5.96 \] square units Rounded to the nearest square unit, it is: \[ 6 \text{ units}^2 \] Thus, the answer is: - ☑ 6 units² - ☐ 24 units² - ☐ 98 units² - ☐ 136 units²
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