Determine the shaded area. 0.5 in.- 1 in. The shaded area is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
8.
![# Determining the Shaded Area
In this exercise, we aim to calculate the shaded area of a geometric figure. The figure presents a blue shaded semicircular region, resembling an arch or a half-donut shape.
## Diagram Details
- **Outer Circle Diameter:** 1 inch
- **Inner Circle Diameter:** 0.5 inches
The diagram shows a semicircle with an outer diameter of 1 inch and an inner, unshaded semicircle with a diameter of 0.5 inches. The shaded area is the region between these two semicircles.
## Calculation
To determine the shaded area:
1. **Calculate the area of the larger semicircle:**
\[
\text{Radius of larger semicircle} = \frac{1}{2} = 0.5 \text{ inches}
\]
\[
\text{Area of full circle (outer)} = \pi \times (0.5)^2
\]
\[
\text{Area of larger semicircle} = \frac{1}{2} \times \pi \times (0.5)^2
\]
2. **Calculate the area of the smaller semicircle:**
\[
\text{Radius of smaller semicircle} = \frac{0.5}{2} = 0.25 \text{ inches}
\]
\[
\text{Area of full circle (inner)} = \pi \times (0.25)^2
\]
\[
\text{Area of smaller semicircle} = \frac{1}{2} \times \pi \times (0.25)^2
\]
3. **Subtract the area of the smaller semicircle from the area of the larger semicircle to find the shaded region:**
\[
\text{Shaded Area} = \left(\frac{1}{2} \times \pi \times (0.5)^2\right) - \left(\frac{1}{2} \times \pi \times (0.25)^2\right)
\]
## Answer
Once calculated, enter the shaded area rounded to the nearest hundredth as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9365df76-a8de-4a84-8e87-8e2e3bbe4302%2Fc01fb8ac-0288-4668-b352-b60d60bb9e0e%2F1qd74z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Determining the Shaded Area
In this exercise, we aim to calculate the shaded area of a geometric figure. The figure presents a blue shaded semicircular region, resembling an arch or a half-donut shape.
## Diagram Details
- **Outer Circle Diameter:** 1 inch
- **Inner Circle Diameter:** 0.5 inches
The diagram shows a semicircle with an outer diameter of 1 inch and an inner, unshaded semicircle with a diameter of 0.5 inches. The shaded area is the region between these two semicircles.
## Calculation
To determine the shaded area:
1. **Calculate the area of the larger semicircle:**
\[
\text{Radius of larger semicircle} = \frac{1}{2} = 0.5 \text{ inches}
\]
\[
\text{Area of full circle (outer)} = \pi \times (0.5)^2
\]
\[
\text{Area of larger semicircle} = \frac{1}{2} \times \pi \times (0.5)^2
\]
2. **Calculate the area of the smaller semicircle:**
\[
\text{Radius of smaller semicircle} = \frac{0.5}{2} = 0.25 \text{ inches}
\]
\[
\text{Area of full circle (inner)} = \pi \times (0.25)^2
\]
\[
\text{Area of smaller semicircle} = \frac{1}{2} \times \pi \times (0.25)^2
\]
3. **Subtract the area of the smaller semicircle from the area of the larger semicircle to find the shaded region:**
\[
\text{Shaded Area} = \left(\frac{1}{2} \times \pi \times (0.5)^2\right) - \left(\frac{1}{2} \times \pi \times (0.25)^2\right)
\]
## Answer
Once calculated, enter the shaded area rounded to the nearest hundredth as needed.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman