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Answer :
To determine the circumference of a circle with a radius of 10 inches, we use the formula for the circumference of a circle which is:
[tex]\[ C = 2 \pi r \][/tex]
Here:
- [tex]\( C \)[/tex] represents the circumference.
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159.
- [tex]\( r \)[/tex] represents the radius of the circle.
Given:
- The radius [tex]\( r \)[/tex] is 10 inches.
Substitute the radius value into the formula:
[tex]\[ C = 2 \times \pi \times 10 \][/tex]
[tex]\[ C = 20 \pi \][/tex]
When you approximate [tex]\( \pi \)[/tex] to 3.14159, you get:
[tex]\[ C \approx 20 \times 3.14159 \][/tex]
This evaluates to:
[tex]\[ C \approx 62.83185307179586 \][/tex]
So, the circumference of the circle is approximately 62.83 inches.
Now, let's look at the available choices:
1. 31.4 inches
2. 49.3 inches
3. 62.8 inches
4. 125.7 inches
The closest value to our calculated circumference of approximately 62.83 inches is 62.8 inches.
Therefore, the correct choice is:
[tex]\[ \boxed{62.8 \text{ inches}} \][/tex]
[tex]\[ C = 2 \pi r \][/tex]
Here:
- [tex]\( C \)[/tex] represents the circumference.
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159.
- [tex]\( r \)[/tex] represents the radius of the circle.
Given:
- The radius [tex]\( r \)[/tex] is 10 inches.
Substitute the radius value into the formula:
[tex]\[ C = 2 \times \pi \times 10 \][/tex]
[tex]\[ C = 20 \pi \][/tex]
When you approximate [tex]\( \pi \)[/tex] to 3.14159, you get:
[tex]\[ C \approx 20 \times 3.14159 \][/tex]
This evaluates to:
[tex]\[ C \approx 62.83185307179586 \][/tex]
So, the circumference of the circle is approximately 62.83 inches.
Now, let's look at the available choices:
1. 31.4 inches
2. 49.3 inches
3. 62.8 inches
4. 125.7 inches
The closest value to our calculated circumference of approximately 62.83 inches is 62.8 inches.
Therefore, the correct choice is:
[tex]\[ \boxed{62.8 \text{ inches}} \][/tex]
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