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

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

Answer 1

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

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

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

3. **Calculate the fraction of the pie that was eaten**:
The total angle in a circle is 360 degrees. The fraction of the pie that was eaten corresponding to an angle of 225° is:
\[
\text{Fraction eaten} = \frac{225}{360} = \frac{5}{8}
\]

4. **Calculate the area of the pie that was eaten**:
Now we can multiply the total area by the fraction eaten:
\[
\text{Area eaten} = \frac{5}{8} \times 25\pi = \frac{125}{8}\pi = 15.625\pi \text{ in}^2
\]

Thus, the area of the pie that was eaten is:

\(\boxed{15.625\pi \text{ in}^2}\)