Answer :
Sure! To find the area and circumference of a circle with a diameter of 12.2 inches, we need to follow these steps:
### Step 1: Calculate the Radius
The radius (r) of a circle is half of its diameter (d).
So, for a diameter of 12.2 inches:
[tex]\[ r = \frac{d}{2} = \frac{12.2}{2} = 6.1 \, \text{inches} \][/tex]
### Step 2: Calculate the Area
The area (A) of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Here, [tex]\( r = 6.1 \)[/tex] inches. Therefore,
[tex]\[ A = \pi \times (6.1)^2 \][/tex]
First, calculate [tex]\( (6.1)^2 \)[/tex]:
[tex]\[ (6.1)^2 = 6.1 \times 6.1 = 37.21 \][/tex]
Now, multiply by [tex]\( \pi \)[/tex] (where [tex]\( \pi \approx 3.14159 \)[/tex]):
[tex]\[ A = 3.14159 \times 37.21 \approx 116.96 \, \text{square inches} \][/tex]
### Step 3: Calculate the Circumference
The circumference (C) of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
Here, [tex]\( r = 6.1 \)[/tex] inches. Therefore,
[tex]\[ C = 2 \times \pi \times 6.1 \][/tex]
Now multiply all the terms together:
[tex]\[ C = 2 \times 3.14159 \times 6.1 \approx 38.32 \, \text{inches} \][/tex]
### Summary
For a circle with a diameter of 12.2 inches:
- The radius is 6.1 inches.
- The area is approximately 116.96 square inches.
- The circumference is approximately 38.32 inches.
Thus, we have:
- Area: [tex]\( 116.96 \, \text{square inches} \)[/tex]
- Circumference: [tex]\( 38.32 \, \text{inches} \)[/tex]
### Step 1: Calculate the Radius
The radius (r) of a circle is half of its diameter (d).
So, for a diameter of 12.2 inches:
[tex]\[ r = \frac{d}{2} = \frac{12.2}{2} = 6.1 \, \text{inches} \][/tex]
### Step 2: Calculate the Area
The area (A) of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Here, [tex]\( r = 6.1 \)[/tex] inches. Therefore,
[tex]\[ A = \pi \times (6.1)^2 \][/tex]
First, calculate [tex]\( (6.1)^2 \)[/tex]:
[tex]\[ (6.1)^2 = 6.1 \times 6.1 = 37.21 \][/tex]
Now, multiply by [tex]\( \pi \)[/tex] (where [tex]\( \pi \approx 3.14159 \)[/tex]):
[tex]\[ A = 3.14159 \times 37.21 \approx 116.96 \, \text{square inches} \][/tex]
### Step 3: Calculate the Circumference
The circumference (C) of a circle is given by the formula:
[tex]\[ C = 2\pi r \][/tex]
Here, [tex]\( r = 6.1 \)[/tex] inches. Therefore,
[tex]\[ C = 2 \times \pi \times 6.1 \][/tex]
Now multiply all the terms together:
[tex]\[ C = 2 \times 3.14159 \times 6.1 \approx 38.32 \, \text{inches} \][/tex]
### Summary
For a circle with a diameter of 12.2 inches:
- The radius is 6.1 inches.
- The area is approximately 116.96 square inches.
- The circumference is approximately 38.32 inches.
Thus, we have:
- Area: [tex]\( 116.96 \, \text{square inches} \)[/tex]
- Circumference: [tex]\( 38.32 \, \text{inches} \)[/tex]
