Question

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

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

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

201.06 in2
201.06

𝑖
𝑛
2
201.06 in2
201.06

𝑖
𝑛
2

505.80 in2
505.80

𝑖
𝑛
2
505.80 in2
505.80

𝑖
𝑛
2

706.86 in2
706.86

𝑖
𝑛
2
706.86 in2
706.86

𝑖
𝑛
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**.