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)ResponsesA=37.5π in.2upper A equals 37.5 pi in. squaredA=25π in.2upper A equals 25 pi in. squaredA=15.625π in.2upper A equals 15.625 pi in. squaredA=9.375π in.2

Answer 1

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

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

2. **Calculate the total area of the pie using the formula for the area of a circle, \( A = \pi r^2 \):**
\[
A = \pi (5)^2 = 25\pi \text{ square inches}
\]

3. **Find the fraction of the pie that was eaten based on the angle:**
The pie is a full circle, which corresponds to \( 360^\circ \). The angle of pie that was eaten is \( 225^\circ \). The fraction of the pie eaten is:
\[
\text{Fraction eaten} = \frac{225}{360} = \frac{5}{8}
\]

4. **Calculate the area of the pie that was eaten:**
\[
\text{Area eaten} = \frac{5}{8} \times \text{Total area} = \frac{5}{8} \times 25\pi = \frac{125\pi}{8} = 15.625\pi \text{ square inches}
\]

Thus, the area of the pie that was eaten is \( \boxed{15.625\pi} \) square inches.