Question

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=25π in.2
upper A equals 25 pi in. squared

A=9.375π in.2
upper A equals 9.375 pi in. squared

A=37.5π in.2
upper A equals 37.5 pi in. squared

A=15.625π in.2

Answer 1

To find the area of the eaten pie, we need to calculate the area of the entire pie first and then find the portion corresponding to the 225° angle.

1. **Calculate the area of the entire pie.**
The formula for the area (A) of a circle is:
\[
A = \pi r^2
\]
The radius (r) of the pie is half of the diameter:
\[
r = \frac{10 \text{ inches}}{2} = 5 \text{ inches}
\]
Now, substituting the radius into the area formula:
\[
A = \pi (5)^2 = 25\pi \text{ in}^2
\]

2. **Find the area corresponding to the eaten slices (225°).**
The entire circle corresponds to \(360°\), and the portion of the pie that was eaten is \(225°\). We find the fraction of the pie that was eaten:
\[
\text{Fraction eaten} = \frac{225°}{360°} = \frac{225}{360} = \frac{5}{8}
\]

Now, calculate the area of the eaten pie:
\[
\text{Area eaten} = \text{Fraction eaten} \times \text{Total area}
\]
\[
\text{Area eaten} = \frac{5}{8} \times 25\pi = \frac{125}{8}\pi \text{ in}^2
\]
\[
\text{Area eaten} = 15.625\pi \text{ in}^2
\]

3. **Conclusion**
Therefore, the area of the pie that was eaten is:
\[
\boxed{15.625\pi \text{ in}^2}
\]