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
Related questions
Question
![**Geometry Problem: Finding the Area of a Sector**
In circle N with \( \angle MNP = 90^\circ \) and \( MN = 12 \) units, find the area of sector MNP. Round to the nearest hundredth.
### Diagram Description
The diagram provided shows a circle with center N. Points M and P are on the circumference of the circle. The angle \( \angle MNP \) is a right angle, i.e., \( 90^\circ \). The radius of the circle, denoted by the length MN, is 12 units.
### Calculations
To find the area of sector MNP, we use the formula for the area of a sector:
\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where \( \theta \) is the angle of the sector and \( r \) is the radius of the circle.
Given:
\[
\theta = 90^\circ
\]
\[
r = 12 \text{ units}
\]
Plugging these values into the formula, we get:
\[
\text{Area of Sector} = \frac{90^\circ}{360^\circ} \times \pi (12)^2
\]
Simplify the fraction:
\[
= \frac{1}{4} \times \pi \times 144
\]
\[
= 36\pi
\]
Using the approximation \( \pi \approx 3.14 \):
\[
\text{Area of Sector} = 36 \times 3.14
\]
\[
\approx 113.04
\]
Therefore, the area of sector MNP is approximately
\[
\boxed{113.04} \text{ square units}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ff36725-3ed3-45b7-b6a0-6c3f24cceeaa%2Fd980d559-1cc2-42b5-a2c3-2ab8c4a0ee96%2F8ceuqxc_processed.png&w=3840&q=75)
Transcribed Image Text:**Geometry Problem: Finding the Area of a Sector**
In circle N with \( \angle MNP = 90^\circ \) and \( MN = 12 \) units, find the area of sector MNP. Round to the nearest hundredth.
### Diagram Description
The diagram provided shows a circle with center N. Points M and P are on the circumference of the circle. The angle \( \angle MNP \) is a right angle, i.e., \( 90^\circ \). The radius of the circle, denoted by the length MN, is 12 units.
### Calculations
To find the area of sector MNP, we use the formula for the area of a sector:
\[ \text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
where \( \theta \) is the angle of the sector and \( r \) is the radius of the circle.
Given:
\[
\theta = 90^\circ
\]
\[
r = 12 \text{ units}
\]
Plugging these values into the formula, we get:
\[
\text{Area of Sector} = \frac{90^\circ}{360^\circ} \times \pi (12)^2
\]
Simplify the fraction:
\[
= \frac{1}{4} \times \pi \times 144
\]
\[
= 36\pi
\]
Using the approximation \( \pi \approx 3.14 \):
\[
\text{Area of Sector} = 36 \times 3.14
\]
\[
\approx 113.04
\]
Therefore, the area of sector MNP is approximately
\[
\boxed{113.04} \text{ square units}
\]
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 1 images
Knowledge Booster
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
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning