The shaded area is (Round to two decimal p d.) ft. ?.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
7.
![**Determine the Shaded Area**
In the image, there is a circle inscribed within a square. The circle has a diameter labeled as 14 ft. The area outside the circle but within the square is shaded.
**Diagram Explanation:**
- The circle is perfectly inscribed within a square, meaning the diameter of the circle is equal to the side length of the square.
- The circle's diameter is indicated as 14 ft, so each side of the square is also 14 ft.
**Task:**
Calculate the area of the shaded region.
**Steps:**
1. **Calculate the Area of the Square:**
\[
\text{Area of square} = \text{side}^2 = 14^2 = 196 \, \text{ft}^2
\]
2. **Calculate the Area of the Circle:**
- Radius of circle = diameter/2 = 14/2 = 7 ft
\[
\text{Area of circle} = \pi \times \text{radius}^2 = \pi \times 7^2 \approx 153.94 \, \text{ft}^2
\]
3. **Calculate the Shaded Area:**
\[
\text{Shaded area} = \text{Area of square} - \text{Area of circle} = 196 - 153.94 \approx 42.06 \, \text{ft}^2
\]
**The shaded area is:** [\_\_] ft²
*(Round to two decimal places.)*
Select the correct unit from the options provided:
- ft.
- ft⁴.
- ft².
- ft³.
The correct choice is ft².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9365df76-a8de-4a84-8e87-8e2e3bbe4302%2F03ae8e88-b971-412a-a077-e4ba85f6d5e1%2F94n6xel_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine the Shaded Area**
In the image, there is a circle inscribed within a square. The circle has a diameter labeled as 14 ft. The area outside the circle but within the square is shaded.
**Diagram Explanation:**
- The circle is perfectly inscribed within a square, meaning the diameter of the circle is equal to the side length of the square.
- The circle's diameter is indicated as 14 ft, so each side of the square is also 14 ft.
**Task:**
Calculate the area of the shaded region.
**Steps:**
1. **Calculate the Area of the Square:**
\[
\text{Area of square} = \text{side}^2 = 14^2 = 196 \, \text{ft}^2
\]
2. **Calculate the Area of the Circle:**
- Radius of circle = diameter/2 = 14/2 = 7 ft
\[
\text{Area of circle} = \pi \times \text{radius}^2 = \pi \times 7^2 \approx 153.94 \, \text{ft}^2
\]
3. **Calculate the Shaded Area:**
\[
\text{Shaded area} = \text{Area of square} - \text{Area of circle} = 196 - 153.94 \approx 42.06 \, \text{ft}^2
\]
**The shaded area is:** [\_\_] ft²
*(Round to two decimal places.)*
Select the correct unit from the options provided:
- ft.
- ft⁴.
- ft².
- ft³.
The correct choice is ft².
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