Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter16: Table Of Decimal Equivalents And Combined Operations Of Decimal Fractions
Section: Chapter Questions
Problem 36A: A slot is machined in a circular plate with a 41.36-millimeter diameter. Two milling cuts, one 6.30...
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![### Problem: Finding the Area of a Circle
**Question:**
What is the area of a circle with a diameter of 22.18? Use π = 3.14 if appropriate.
(round to two decimal places as needed)
**Solution:**
To find the area of a circle, we use the formula:
\[ \text{Area} = \pi r^2 \]
Where \( \pi \approx 3.14 \) and \( r \) is the radius of the circle. The radius is half of the diameter.
Given:
- Diameter \(d = 22.18\)
First, we find the radius \(r\):
\[ r = \frac{d}{2} = \frac{22.18}{2} = 11.09 \]
Now, we substitute the radius \(r\) and \( \pi \) into the area formula:
\[ \text{Area} = 3.14 \times (11.09)^2 \]
Calculating \( (11.09)^2 \):
\[ (11.09)^2 = 123.4881 \]
Now, multiplying by \( \pi \) (3.14):
\[ \text{Area} = 3.14 \times 123.4881 = 387.76 \]
So, the area of the circle is:
\[ \text{Area} \approx 387.76 \, \text{square units} \]
**Answer:**
The area of the circle is approximately 387.76 square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91652952-972c-437d-817e-6a9e046f1c10%2F87a07eae-6fa2-4c65-8394-6cf387a78f33%2Faqnbl8b_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem: Finding the Area of a Circle
**Question:**
What is the area of a circle with a diameter of 22.18? Use π = 3.14 if appropriate.
(round to two decimal places as needed)
**Solution:**
To find the area of a circle, we use the formula:
\[ \text{Area} = \pi r^2 \]
Where \( \pi \approx 3.14 \) and \( r \) is the radius of the circle. The radius is half of the diameter.
Given:
- Diameter \(d = 22.18\)
First, we find the radius \(r\):
\[ r = \frac{d}{2} = \frac{22.18}{2} = 11.09 \]
Now, we substitute the radius \(r\) and \( \pi \) into the area formula:
\[ \text{Area} = 3.14 \times (11.09)^2 \]
Calculating \( (11.09)^2 \):
\[ (11.09)^2 = 123.4881 \]
Now, multiplying by \( \pi \) (3.14):
\[ \text{Area} = 3.14 \times 123.4881 = 387.76 \]
So, the area of the circle is:
\[ \text{Area} \approx 387.76 \, \text{square units} \]
**Answer:**
The area of the circle is approximately 387.76 square units.
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