Question

Shavonne is decorating a wreath that has an outer diameter of 22 in. and an inner diameter of 18 in. What is the maximum area of the wreath that she can cover with decorations?(1 point)
Responses

634.60 in.2
634.60 in. squared

125.66 in.2
125.66 in. squared

254.47 in.2
254.47 in. squared

380.13 in.2

Answer 1

To find the maximum area of the wreath that Shavonne can cover with decorations, we first calculate the area of the outer circle and then subtract the area of the inner circle.

1. **Calculate the radius of the outer circle:**
- Outer diameter = 22 inches
- Radius of the outer circle = \( \frac{22}{2} = 11 \) inches

2. **Calculate the radius of the inner circle:**
- Inner diameter = 18 inches
- Radius of the inner circle = \( \frac{18}{2} = 9 \) inches

3. **Calculate the area of the outer circle:**
\[
\text{Area}_{\text{outer}} = \pi r^2 = \pi (11)^2 = 121\pi
\]

4. **Calculate the area of the inner circle:**
\[
\text{Area}_{\text{inner}} = \pi r^2 = \pi (9)^2 = 81\pi
\]

5. **Calculate the area of the wreath:**
\[
\text{Area}_{\text{wreath}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 121\pi - 81\pi = 40\pi
\]

6. **Now, calculate the numerical value using \( \pi \approx 3.14 \):**
\[
40\pi \approx 40 \times 3.14 \approx 125.6 \text{ in}^2
\]

Thus, the maximum area of the wreath that Shavonne can cover with decorations is approximately \( 125.66 \) in².

So the correct response is:
**125.66 in.²**