Question
A)Rajeet’s pumpkin pie is 10 inches in diameter. His family eats five out of the eight slices of pie, forming an angle of 225°. What area of the pie that was eaten?(1 point)
Responses
A=15.625π in.2
upper A equals 15.625 pi in. squared
A=9.375π in.2
upper A equals 9.375 pi in. squared
A=25π in.2
upper A equals 25 pi in. squared
A=37.5π in.2
Responses
A=15.625π in.2
upper A equals 15.625 pi in. squared
A=9.375π in.2
upper A equals 9.375 pi in. squared
A=25π in.2
upper A equals 25 pi in. squared
A=37.5π in.2
Answers
GPT-4o mini
To find the area of the pumpkin pie that was eaten, we first need to determine the total area of the pie and the fraction that corresponds to the 225° angle.
1. **Calculate the total area of the pie:**
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
The radius \( r \) of the pumpkin pie is half of the diameter:
\[
r = \frac{10}{2} = 5 \text{ inches}
\]
Now, we calculate the area:
\[
A = \pi (5)^2 = 25\pi \text{ in}^2
\]
2. **Determine the fraction of the pie that corresponds to the angle of 225°:**
The total angle in a circle is 360°. The fraction of the circle represented by 225° is:
\[
\frac{225}{360} = \frac{5}{8}
\]
3. **Calculate the area of the pie that was eaten:**
To find the area that corresponds to the angle of 225°, multiply the total area of the pie by the fraction of the circle:
\[
A_{eaten} = A \times \frac{5}{8} = 25\pi \times \frac{5}{8}
\]
Performing the calculation:
\[
A_{eaten} = \frac{125\pi}{8} \text{ in}^2
\]
To find the decimal equivalent:
\[
\frac{125}{8} = 15.625
\]
Thus, the area of the pie that was eaten is:
\[
A_{eaten} = 15.625\pi \text{ in}^2
\]
Based on the available choices, the correct answer is:
**A=15.625π in.²**.
1. **Calculate the total area of the pie:**
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
The radius \( r \) of the pumpkin pie is half of the diameter:
\[
r = \frac{10}{2} = 5 \text{ inches}
\]
Now, we calculate the area:
\[
A = \pi (5)^2 = 25\pi \text{ in}^2
\]
2. **Determine the fraction of the pie that corresponds to the angle of 225°:**
The total angle in a circle is 360°. The fraction of the circle represented by 225° is:
\[
\frac{225}{360} = \frac{5}{8}
\]
3. **Calculate the area of the pie that was eaten:**
To find the area that corresponds to the angle of 225°, multiply the total area of the pie by the fraction of the circle:
\[
A_{eaten} = A \times \frac{5}{8} = 25\pi \times \frac{5}{8}
\]
Performing the calculation:
\[
A_{eaten} = \frac{125\pi}{8} \text{ in}^2
\]
To find the decimal equivalent:
\[
\frac{125}{8} = 15.625
\]
Thus, the area of the pie that was eaten is:
\[
A_{eaten} = 15.625\pi \text{ in}^2
\]
Based on the available choices, the correct answer is:
**A=15.625π in.²**.