Madeline wants to plant flowers in a circle at the base of a tree. The tree has a diameter of 16 in

Question

16

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, and Madeline wants the flower bed to have a diameter of 30 in
30

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. What area will the flower bed cover? Round your answer to the nearest hundredth.(1 point)
Responses

201.06 in2
201.06

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2
201.06 in2
201.06

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2

505.80 in2
505.80

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2
505.80 in2
505.80

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2

706.86 in2
706.86

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2
706.86 in2
706.86

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2

907.92 in2

Answer 1

To find the area of the flower bed that Madeline wants to plant, we'll use the formula for the area of a circle:

\[ A = \pi r^2 \]

where \( r \) is the radius of the circle.

1. Determine the radius of the flower bed: The diameter of the flower bed is 30 inches, so the radius \( r \) is: \[ r = \frac{30}{2} = 15 \text{ inches} \]

2. Calculate the area of the flower bed: \[ A = \pi (15)^2 \] \[ A = \pi (225) \] \[ A \approx 3.14159 \times 225 \approx 706.85775 \text{ in}^2 \]

3. Round the area to the nearest hundredth: When rounded, the area is: \[ A \approx 706.86 \text{ in}^2 \]

Thus, the area the flower bed will cover is approximately 706.86 in².

Among the given responses, the correct one is:

706.86 in².