Question

Madeline wants to plant flowers in a circle at the base of a tree. The tree has a diameter of 16 in., and Madeline wants the flower bed to have a diameter of 30 in. What area will the flower bed cover? Round your answer to the nearest hundredth.

Answer 1

To find the area that Madeline's flower bed will cover, we start by noting that the flower bed is shaped like a circle.

The diameter of the flower bed is given as 30 inches. We can find the radius by dividing the diameter by 2:

\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{30 \text{ in.}}{2} = 15 \text{ in.}
\]

Next, we can use the formula for the area of a circle, which is given by:

\[
\text{Area} = \pi r^2
\]

where \( r \) is the radius. Plugging in the radius we just calculated:

\[
\text{Area} = \pi (15 \text{ in.})^2
\]

Calculating \( (15)^2 \):

\[
(15)^2 = 225
\]

Now, substituting back into the area formula:

\[
\text{Area} = \pi \cdot 225
\]

Using the approximation \( \pi \approx 3.14 \):

\[
\text{Area} \approx 3.14 \cdot 225
\]

Calculating this product:

\[
3.14 \cdot 225 \approx 706.5
\]

Thus, rounding to the nearest hundredth, the area that the flower bed will cover is:

\[
\text{Area} \approx 706.50 \text{ in}^2.
\]

Therefore, the area of the flower bed is

\[
\boxed{706.50} \text{ in}^2.
\]