To determine the number of flowers needed to surround a circular garden with a radius of 10 feet, spaced every 6 inches, we can follow these steps:
1. Convert the radius from feet to inches:
The radius of the garden is given as 10 feet. Since there are 12 inches in a foot, we convert the radius to inches by multiplying:
[tex]\[
\text{Radius in inches} = 10 \, \text{feet} \times 12 \, \text{inches/foot} = 120 \, \text{inches}
\][/tex]
2. Calculate the circumference of the garden:
The circumference [tex]\(C\)[/tex] of a circle is given by the formula [tex]\(C = 2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle.
[tex]\[
\text{Circumference} = 2 \times \pi \times 120 \, \text{inches} \approx 753.98 \, \text{inches}
\][/tex]
3. Determine the number of flowers needed:
Flowers are to be spaced every 6 inches along the circumference. We calculate the number of flowers by dividing the circumference by the spacing distance:
[tex]\[
\text{Number of flowers} = \frac{\text{Circumference}}{\text{Spacing}} = \frac{753.98 \, \text{inches}}{6 \, \text{inches/flower}} \approx 125.66
\][/tex]
4. Round to the nearest whole number:
Since you cannot have a fraction of a flower, we round the result to the nearest whole number:
[tex]\[
\text{Number of flowers (rounded)} \approx 126
\][/tex]
Therefore, you would need approximately 126 flowers, spaced every 6 inches, to surround the circular garden with a 10-foot radius.
