Question

enge How many flowers, spaced every 4 in., are needed to surround a circular garden with a 150-ft radius? Use 3.14
wers are needed to surround the circular garden.

Answer 1

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:

$\[ \text{Radius in inches} = 150 \text{ feet} \times 12 \text{ inches/foot} = 1800 \text{ inches} \]$

Step 2: Calculate the circumference of the garden

The formula for the circumference $\( C \)$ of a circle is given by:

$\[ C = 2 \pi r \]$

Where $\( r \)$ is the radius of the circle and $\( \pi \)$ is approximately 3.14. Plugging in our values:

$\[ C = 2 \times 3.14 \times 1800 \text{ inches} \]$
$\[ C = 6.28 \times 1800 \text{ inches} \]$
$\[ C = 11304 \text{ inches} \]$

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:

$\[ \text{Number of flowers} = \frac{\text{Circumference}}{\text{Spacing}} \]$
$\[ \text{Number of flowers} = \frac{11304 \text{ inches}}{4 \text{ inches/flower}} \]$
$\[ \text{Number of flowers} = 2826 \]$

Hence, 2826 flowers are needed to surround the circular garden.