Question

 How many​ flowers, spaced every 4 ​in., are needed to surround a circular garden with a 150​-ft ​radius? Use 3.14 for pi.
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Part 1
  
enter your response here flowers are needed to surround the circular garden.

Answer 1

To find out how many flowers are needed to surround a circular garden with a radius of 150 feet, we first need to calculate the circumference of the garden using the formula:

\[
C = 2\pi r
\]

where \( r \) is the radius and \( \pi \) is approximately 3.14.

1. **Calculate the circumference**:
\[
C = 2 \times 3.14 \times 150
\]
\[
C = 6.28 \times 150
\]
\[
C = 942 \text{ feet}
\]

2. **Determine the spacing between the flowers**:
The flowers are spaced every 4 inches. We need to convert the circumference from feet to inches, knowing that there are 12 inches in a foot:
\[
942 \text{ feet} = 942 \times 12 \text{ inches} = 11304 \text{ inches}
\]

3. **Calculate how many flowers are needed**:
To find the number of flowers, divide the total circumference in inches by the spacing in inches:
\[
\text{Number of flowers} = \frac{\text{Circumference in inches}}{\text{Spacing in inches}} = \frac{11304}{4}
\]
\[
\text{Number of flowers} = 2826
\]

Therefore, **2826 flowers** are needed to surround the circular garden.