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

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

A=15.625π in.2

Answer 1

To find the area of the pumpkin pie that was eaten, we can use the formula for the area of a sector of a circle. The formula for the area \(A\) of a sector is given by:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

where:
- \(\theta\) is the angle of the sector in degrees,
- \(r\) is the radius of the circle.

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

2. **Plug the values into the sector area formula**:
Given that the family eats a portion that forms an angle of 225°, we can substitute \(\theta = 225^\circ\) and \(r = 5\):

\[
A = \frac{225}{360} \times \pi (5^2)
\]

3. **Calculate \(5^2\)**:
\[
5^2 = 25
\]

4. **Substitute and solve for \(A\)**:
\[
A = \frac{225}{360} \times \pi \times 25
\]
Simplifying \(\frac{225}{360}\):
\[
\frac{225}{360} = \frac{225 \div 45}{360 \div 45} = \frac{5}{8}
\]

So, we can rewrite the area as:
\[
A = \frac{5}{8} \times \pi \times 25 = \frac{125}{8} \pi
\]

5. **Calculate \(\frac{125}{8}\)**:
\[
\frac{125}{8} = 15.625
\]

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

\[
A = 15.625\pi \text{ in}^2
\]

**The correct answer is:**
A=15.625π in.²