Homework Help is Here – Start Your Trial Now!
Math
Geometry
Find the area of the shaded segments. Leave your answers in terms of A. 10. 11. 12. 120° 60°

Find the area of the shaded segments. Leave your answers in terms of A. 10. 11. 12. 120° 60°

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
See similar textbooks
Question

Find the area of the shaded regions. Round all answers to the nearest 10th.

## Calculate the Area of the Shaded Segments ### Instructions: For each of the following circles, find the area of the shaded segment. Leave your answers in terms of \(\pi\). ### Problems: 1. **Problem 10:** - Diagram: A circle with a radius of 2 units. A sector is shaded, with the central angle forming a right angle (90 degrees). 2. **Problem 11:** - Diagram: A circle with a radius of 4 units. A sector is shaded, with the central angle measuring 120 degrees. 3. **Problem 12:** - Diagram: A circle with a radius of 1 unit. A sector is shaded, with the central angle measuring 60 degrees. ### Explanation of Diagrams: - **Problem 10:** The shaded area is a quarter circle, as indicated by the 90-degree central angle. The radius of the circle is 2 units. - **Problem 11:** The shaded area corresponds to a sector of the circle with a central angle of 120 degrees. The radius of this circle is 4 units. - **Problem 12:** The shaded segment is a sector with a central angle of 60 degrees. The radius of the circle is 1 unit. Use the formula for the area of a sector, \(\text{Area} = \frac{\theta}{360} \times \pi r^2\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle, to find the areas of the shaded segments. For each problem, calculate the sector area using the provided angles and radii.
Transcribed Image Text:## Calculate the Area of the Shaded Segments ### Instructions: For each of the following circles, find the area of the shaded segment. Leave your answers in terms of \(\pi\). ### Problems: 1. **Problem 10:** - Diagram: A circle with a radius of 2 units. A sector is shaded, with the central angle forming a right angle (90 degrees). 2. **Problem 11:** - Diagram: A circle with a radius of 4 units. A sector is shaded, with the central angle measuring 120 degrees. 3. **Problem 12:** - Diagram: A circle with a radius of 1 unit. A sector is shaded, with the central angle measuring 60 degrees. ### Explanation of Diagrams: - **Problem 10:** The shaded area is a quarter circle, as indicated by the 90-degree central angle. The radius of the circle is 2 units. - **Problem 11:** The shaded area corresponds to a sector of the circle with a central angle of 120 degrees. The radius of this circle is 4 units. - **Problem 12:** The shaded segment is a sector with a central angle of 60 degrees. The radius of the circle is 1 unit. Use the formula for the area of a sector, \(\text{Area} = \frac{\theta}{360} \times \pi r^2\), where \(\theta\) is the central angle in degrees and \(r\) is the radius of the circle, to find the areas of the shaded segments. For each problem, calculate the sector area using the provided angles and radii.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Area of a Circle
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS