Terms Use Calculator The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? O 12+18.25 units² O 24+9.1257 units² O 24+18.257 units² O 12+9.125 units² 4-3-2-¹1. 4 2 1 1 -2+ -3+ -5+ 2 1 2 3 3 4 4 5 6 5 ➜X (O) 6 7
Terms Use Calculator The curved part of this figure is a semicircle. What is the best approximation for the area of this figure? O 12+18.25 units² O 24+9.1257 units² O 24+18.257 units² O 12+9.125 units² 4-3-2-¹1. 4 2 1 1 -2+ -3+ -5+ 2 1 2 3 3 4 4 5 6 5 ➜X (O) 6 7
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
Related questions
Question
![### Calculating the Area of a Combined Figure
**Problem Statement:**
The curved part of this figure is a semicircle.
**Question:**
What is the best approximation for the area of this figure?
**Answer Choices:**
- O 12 + 18.25π units²
- O 24 + 9.125π units²
- O 24 + 18.25π units²
- O 12 + 9.125π units²
**Diagram Explanation:**
The accompanying diagram shows a coordinate plane with a combined shape consisting of a square and a semicircle. The square is positioned with its bottom-left corner at (-3, -3) and extends to (3, 3), making the side length of the square 6 units. The semicircle is placed on the top side of the square.
**Steps to Approximate the Area:**
1. **Calculate the Area of the Square:**
- Side length = 6 units
- Area of the square = side length² = 6² = 36 units²
2. **Calculate the Area of the Semicircle:**
- Diameter of the semicircle = side length of the square = 6 units
- Radius of the semicircle = diameter / 2 = 6 / 2 = 3 units
- Area of a full circle = π * radius² = π * (3)² = 9π units²
- Area of the semicircle = (1/2) * Area of the full circle = (1/2) * 9π = 4.5π units²
3. **Combine the Areas:**
- Total area = Area of the square + Area of the semicircle = 36 units² + 4.5π units²
**Multiple Choice Concept:**
When selecting the best approximation for the area, identify the correct combination of constants and π terms that closely match the calculation above.
The correct answer should consider both the square's area (36 units²) and the semicircle's area (4.5π units²).
**Answer:**
Thus, the closest match for the area is:
- **24 + 18.25π units²**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b717370-ac2a-4449-94d5-6954bef42bac%2F2049d2c7-969a-4ed4-93f9-d04974350667%2F8zou47h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Area of a Combined Figure
**Problem Statement:**
The curved part of this figure is a semicircle.
**Question:**
What is the best approximation for the area of this figure?
**Answer Choices:**
- O 12 + 18.25π units²
- O 24 + 9.125π units²
- O 24 + 18.25π units²
- O 12 + 9.125π units²
**Diagram Explanation:**
The accompanying diagram shows a coordinate plane with a combined shape consisting of a square and a semicircle. The square is positioned with its bottom-left corner at (-3, -3) and extends to (3, 3), making the side length of the square 6 units. The semicircle is placed on the top side of the square.
**Steps to Approximate the Area:**
1. **Calculate the Area of the Square:**
- Side length = 6 units
- Area of the square = side length² = 6² = 36 units²
2. **Calculate the Area of the Semicircle:**
- Diameter of the semicircle = side length of the square = 6 units
- Radius of the semicircle = diameter / 2 = 6 / 2 = 3 units
- Area of a full circle = π * radius² = π * (3)² = 9π units²
- Area of the semicircle = (1/2) * Area of the full circle = (1/2) * 9π = 4.5π units²
3. **Combine the Areas:**
- Total area = Area of the square + Area of the semicircle = 36 units² + 4.5π units²
**Multiple Choice Concept:**
When selecting the best approximation for the area, identify the correct combination of constants and π terms that closely match the calculation above.
The correct answer should consider both the square's area (36 units²) and the semicircle's area (4.5π units²).
**Answer:**
Thus, the closest match for the area is:
- **24 + 18.25π units²**
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 3 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL