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Chapter 10: Problem 49

How many plants spaced every 6 inches are needed to surround a circular garden with a 30 -foot radius?

Short Answer

Expert verified
The gardener will require approximately 377 plants to surround the garden with plants spaced every 6 inches.

Step by step solution

01

Convert feet to inches

Since the radius is given in feet and the plant spacing is in inches, first convert the radius from feet to inches. There are 12 inches in a foot, so multiply the radius in feet by 12. \( Radius_{inches} = 30 * 12 = 360 \) inches
02

Calculate the circumference of the circle

The formula for the circumference of a circle is \( C = 2 \pi r \), where \( r \) is the radius. Plugging in the radius calculated in inches: \( C = 2 \pi * 360 \)
03

Determine the number of plants

The number of plants needed can be calculated by dividing the circumference by the space needed for each plant. Therefore, \( Number_{plants} = \frac{C}{spacing_{plants}} = \frac{2 \pi * 360}{6} \)

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