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.
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Calculate the circumference: \[ C = 2 \times 3.14 \times 150 \] \[ C = 6.28 \times 150 \] \[ C = 942 \text{ feet} \]
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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: \[ 942 \text{ feet} = 942 \times 12 \text{ inches} = 11304 \text{ inches} \]
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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.