Suppose you are given a square with an inscribed circle as shown below. If the area of the square is 144 m² what is the area of the circle? (Use 3.14159 for .)
Suppose you are given a square with an inscribed circle as shown below. If the area of the square is 144 m² what is the area of the circle? (Use 3.14159 for .)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
### Diagram
A square with a circle inscribed in it. The circle touches all four sides of the square.
#### Given:
- Area of the square = 144 m²
### Solution
First, we need to find the side length of the square. The area \( A \) of a square is given by:
\[ A = \text{side}^2 \]
So, the side length of the square is:
\[ \text{side} = \sqrt{A} = \sqrt{144} = 12 \, \text{m} \]
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diameter \( D \) of the circle is:
\[ D = 12 \, \text{m} \]
The radius \( r \) of the circle is half of the diameter:
\[ r = \frac{D}{2} = \frac{12}{2} = 6 \, \text{m} \]
The area \( A_{\text{circle}} \) of the circle is given by:
\[ A_{\text{circle}} = \pi r^2 \]
Using 3.14159 for \( \pi \):
\[ A_{\text{circle}} = 3.14159 \times (6)^2 = 3.14159 \times 36 = 113.10 \, \text{m}^2 \]
### Answer:
\[ \text{The area of the circle is } 113.10 \, \text{m}^2 \, (\text{Write your answer to two decimal places.}) \]
---
#### Notes
- Time Remaining: 00:59:06
- Buttons: "Next"
This problem can be utilized in the context of understanding geometric shapes and their properties, specifically focusing on the relationships between squares and circles inscribed in them.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bb6fa2-16f6-449b-8672-e576ef2a7d16%2F40f52977-a244-48ce-8df0-0a3282a0579c%2F8693csr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Suppose you are given a square with an inscribed circle as shown below. If the area of the square is 144 m², what is the area of the circle? (Use 3.14159 for π.)
### Diagram
A square with a circle inscribed in it. The circle touches all four sides of the square.
#### Given:
- Area of the square = 144 m²
### Solution
First, we need to find the side length of the square. The area \( A \) of a square is given by:
\[ A = \text{side}^2 \]
So, the side length of the square is:
\[ \text{side} = \sqrt{A} = \sqrt{144} = 12 \, \text{m} \]
Since the circle is inscribed in the square, the diameter of the circle is equal to the side length of the square. Therefore, the diameter \( D \) of the circle is:
\[ D = 12 \, \text{m} \]
The radius \( r \) of the circle is half of the diameter:
\[ r = \frac{D}{2} = \frac{12}{2} = 6 \, \text{m} \]
The area \( A_{\text{circle}} \) of the circle is given by:
\[ A_{\text{circle}} = \pi r^2 \]
Using 3.14159 for \( \pi \):
\[ A_{\text{circle}} = 3.14159 \times (6)^2 = 3.14159 \times 36 = 113.10 \, \text{m}^2 \]
### Answer:
\[ \text{The area of the circle is } 113.10 \, \text{m}^2 \, (\text{Write your answer to two decimal places.}) \]
---
#### Notes
- Time Remaining: 00:59:06
- Buttons: "Next"
This problem can be utilized in the context of understanding geometric shapes and their properties, specifically focusing on the relationships between squares and circles inscribed in them.
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 with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning