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=15.625π in.2
upper A equals 15.625 pi in. squared

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

Answer 1

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

1. **Calculate the radius of the pie**:
Since the diameter of the pie is 10 inches, the radius \( r \) is:
\[
r = \frac{10}{2} = 5 \text{ inches}
\]

2. **Calculate the area of the entire pie**:
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Substituting the radius:
\[
A = \pi (5^2) = 25\pi \text{ in}^2
\]

3. **Calculate the area of the pie that was eaten**:
The fraction of the pie that was eaten corresponds to the angle consumed:
\[
\text{Fraction eaten} = \frac{225°}{360°} = \frac{225}{360} = \frac{5}{8}
\]

Now, we multiply the total area by this fraction to find the eaten area:
\[
\text{Area eaten} = \frac{5}{8} \times 25\pi = \frac{125}{8}\pi \text{ in}^2
\]

Calculating \( \frac{125}{8} \):
\[
\frac{125}{8} = 15.625
\]
So,
\[
\text{Area eaten} = 15.625\pi \text{ in}^2
\]

Therefore, the area of the pie that was eaten is \( A = 15.625\pi \text{ in}^2 \). The correct response is:
**A = 15.625π in²**.