Question
Find the shaded area. Note that this exercise contains a semicircle. Use 3.14 as the approximate value of pi.
9 in.
Question content area bottom
Part 1
The shaded area is approximately
enter your response here
▼
in.
in. squared .
(Round to the nearest tenth as needed.)
9 in.
Question content area bottom
Part 1
The shaded area is approximately
enter your response here
▼
in.
in. squared .
(Round to the nearest tenth as needed.)
Answers
GPT-4o mini
To find the shaded area that involves a semicircle, we need to first calculate the area of the semicircle and then determine the shaded area based on the context, which has not been provided in your prompt. However, I will assume you're looking to find the area of a semicircle with a diameter of 9 inches.
1. **Find the radius**: The radius (r) of the semicircle is half of the diameter.
\[
r = \frac{9}{2} = 4.5 \text{ inches}
\]
2. **Calculate the area of the semicircle**: The formula for the area of a circle is \( \pi r^2 \). Since we need the area of a semicircle, we will divide this by 2:
\[
\text{Area of semicircle} = \frac{1}{2} \pi r^2
\]
3. **Substitute the values**: Using \( \pi \approx 3.14 \) and \( r = 4.5 \):
\[
\text{Area of semicircle} = \frac{1}{2} \times 3.14 \times (4.5)^2
\]
\[
= \frac{1}{2} \times 3.14 \times 20.25
\]
\[
= \frac{1}{2} \times 63.435
\]
\[
\approx 31.7175
\]
4. **Round to the nearest tenth**:
\[
31.7175 \approx 31.7
\]
Thus, the shaded area of the semicircle is approximately **31.7 in²**. If there are additional segments or figures that contribute to the shaded area, please provide details for a more accurate answer.
1. **Find the radius**: The radius (r) of the semicircle is half of the diameter.
\[
r = \frac{9}{2} = 4.5 \text{ inches}
\]
2. **Calculate the area of the semicircle**: The formula for the area of a circle is \( \pi r^2 \). Since we need the area of a semicircle, we will divide this by 2:
\[
\text{Area of semicircle} = \frac{1}{2} \pi r^2
\]
3. **Substitute the values**: Using \( \pi \approx 3.14 \) and \( r = 4.5 \):
\[
\text{Area of semicircle} = \frac{1}{2} \times 3.14 \times (4.5)^2
\]
\[
= \frac{1}{2} \times 3.14 \times 20.25
\]
\[
= \frac{1}{2} \times 63.435
\]
\[
\approx 31.7175
\]
4. **Round to the nearest tenth**:
\[
31.7175 \approx 31.7
\]
Thus, the shaded area of the semicircle is approximately **31.7 in²**. If there are additional segments or figures that contribute to the shaded area, please provide details for a more accurate answer.