To determine the number of flowers needed to surround a circular garden with a radius of 150 feet, given that the flowers are spaced every 4 inches, we will follow these steps:
1. Convert the radius from feet to inches.
2. Calculate the circumference of the circular garden.
3. Calculate the number of flowers needed based on the spacing.
### Step-by-Step Solution:
Step 1: Convert the radius from feet to inches
We know that 1 foot is equivalent to 12 inches. Therefore, the radius in inches is:
[tex]\[ \text{Radius in inches} = 150 \text{ feet} \times 12 \text{ inches/foot} = 1800 \text{ inches} \][/tex]
Step 2: Calculate the circumference of the garden
The formula for the circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
Where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \pi \)[/tex] is approximately 3.14. Plugging in our values:
[tex]\[ C = 2 \times 3.14 \times 1800 \text{ inches} \][/tex]
[tex]\[ C = 6.28 \times 1800 \text{ inches} \][/tex]
[tex]\[ C = 11304 \text{ inches} \][/tex]
Step 3: Calculate the number of flowers needed
The flowers are spaced every 4 inches. To find the number of flowers, we divide the circumference by the spacing:
[tex]\[ \text{Number of flowers} = \frac{\text{Circumference}}{\text{Spacing}} \][/tex]
[tex]\[ \text{Number of flowers} = \frac{11304 \text{ inches}}{4 \text{ inches/flower}} \][/tex]
[tex]\[ \text{Number of flowers} = 2826 \][/tex]
Hence, 2826 flowers are needed to surround the circular garden.
