To find the radius of a circular garden given its circumference, you can use the formula for the circumference of a circle:
[tex]\[ C = 2 \pi r \][/tex]
Where:
- [tex]\( C \)[/tex] is the circumference
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14
- [tex]\( r \)[/tex] is the radius of the circle
Given:
- The circumference ([tex]\( C \)[/tex]) is 144.44 feet.
- [tex]\( \pi \)[/tex] is 3.14.
You need to solve for the radius ([tex]\( r \)[/tex]).
Steps:
1. Start with the formula for the circumference of a circle:
[tex]\[ C = 2 \pi r \][/tex]
2. Substitute the given values into the formula:
[tex]\[ 144.44 = 2 \cdot 3.14 \cdot r \][/tex]
3. To isolate [tex]\( r \)[/tex], divide both sides of the equation by [tex]\( 2 \pi \)[/tex]:
[tex]\[ r = \frac{144.44}{2 \cdot 3.14} \][/tex]
4. Calculate the denominator:
[tex]\[ 2 \cdot 3.14 = 6.28 \][/tex]
5. Now, divide the circumference by this value:
[tex]\[ r = \frac{144.44}{6.28} \][/tex]
6. Performing the division:
[tex]\[ r = 23.0 \][/tex]
Therefore, the radius of the garden is 23.0 feet.
