Question
page 14 of 14 Area of a Model Quick Check 2 of 52 of 5 Items 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 125.66 in.2 125.66 in. squared 254.47 in.2 254.47 in. squared 380.13 in.2 380.13 in. squared 634.60 in.2 634.60 in. squared Skip to navigation
Answers
GPT-4o mini
To find the maximum area of the wreath that Shavonne can cover with decorations, we need to calculate the area of the outer circle and subtract the area of the inner circle.
1. **Calculate the radius of the outer circle:**
\[
\text{Outer radius} = \frac{\text{Outer diameter}}{2} = \frac{22 \text{ in}}{2} = 11 \text{ in}
\]
2. **Calculate the radius of the inner circle:**
\[
\text{Inner radius} = \frac{\text{Inner diameter}}{2} = \frac{18 \text{ in}}{2} = 9 \text{ in}
\]
3. **Calculate the area of the outer circle:**
\[
\text{Area}_{\text{outer}} = \pi \times (\text{Outer radius})^2 = \pi \times (11 \text{ in})^2 = \pi \times 121 \text{ in}^2 \approx 380.13 \text{ in}^2
\]
4. **Calculate the area of the inner circle:**
\[
\text{Area}_{\text{inner}} = \pi \times (\text{Inner radius})^2 = \pi \times (9 \text{ in})^2 = \pi \times 81 \text{ in}^2 \approx 254.47 \text{ in}^2
\]
5. **Calculate the area of the wreath:**
\[
\text{Area}_{\text{wreath}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} \approx 380.13 \text{ in}^2 - 254.47 \text{ in}^2 \approx 125.66 \text{ in}^2
\]
Thus, the maximum area of the wreath that she can cover with decorations is approximately **125.66 in²**.
The correct response is: **125.66 in.²** (or **125.66 in squared**).
1. **Calculate the radius of the outer circle:**
\[
\text{Outer radius} = \frac{\text{Outer diameter}}{2} = \frac{22 \text{ in}}{2} = 11 \text{ in}
\]
2. **Calculate the radius of the inner circle:**
\[
\text{Inner radius} = \frac{\text{Inner diameter}}{2} = \frac{18 \text{ in}}{2} = 9 \text{ in}
\]
3. **Calculate the area of the outer circle:**
\[
\text{Area}_{\text{outer}} = \pi \times (\text{Outer radius})^2 = \pi \times (11 \text{ in})^2 = \pi \times 121 \text{ in}^2 \approx 380.13 \text{ in}^2
\]
4. **Calculate the area of the inner circle:**
\[
\text{Area}_{\text{inner}} = \pi \times (\text{Inner radius})^2 = \pi \times (9 \text{ in})^2 = \pi \times 81 \text{ in}^2 \approx 254.47 \text{ in}^2
\]
5. **Calculate the area of the wreath:**
\[
\text{Area}_{\text{wreath}} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} \approx 380.13 \text{ in}^2 - 254.47 \text{ in}^2 \approx 125.66 \text{ in}^2
\]
Thus, the maximum area of the wreath that she can cover with decorations is approximately **125.66 in²**.
The correct response is: **125.66 in.²** (or **125.66 in squared**).