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 in2 ​A=15.625π in2 ​A=9.375π in2 ​A=9.375π in2 ​A=25π in2 ​A=25π in2 ​A=37.5π in2

Answer 1

To calculate the area of the pumpkin pie that was eaten, we first determine the area of the entire pie and then find the fraction of that area corresponding to the 225° angle that represents the portion eaten.

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

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

3. **Determine the fraction of the pie eaten**:
Since Rajeet's family ate a portion that corresponds to 225°, we find the fraction of the pie eaten compared to the total angle in a circle (360°):
\[
\text{Fraction eaten} = \frac{225°}{360°} = \frac{225}{360} = \frac{5}{8}
\]

4. **Calculate the area of the pie that was eaten**:
Multiply the total area of the pie by the fraction that was eaten:
\[
A_{eaten} = A \times \text{Fraction eaten} = 25\pi \times \frac{5}{8}
\]

Calculating this gives:
\[
A_{eaten} = 25\pi \times \frac{5}{8} = \frac{125\pi}{8}
\]
To approximate \( \frac{125}{8} \):
\[
\frac{125}{8} = 15.625
\]

Thus, the area of pie that was eaten is:
\[
A_{eaten} = 15.625\pi \text{ square inches}
\]

Finally, the correct answer is:
**A = 15.625π in²**.