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=37.5π in.2
upper A equals 37.5 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 pumpkin pie that was eaten, we can use the formula for the area of a circle and the proportion of the pie that was eaten based on the angle.

1. **Calculate the total area of the pie**:
The formula for the area \( A \) of a circle is given by:
\[
A = \pi r^2
\]
where \( r \) is the radius. Since the diameter is 10 inches, the radius \( r \) is half of the diameter:
\[
r = \frac{10}{2} = 5 \text{ inches}
\]
Now, plug in the radius to find the area:
\[
A = \pi (5)^2 = 25\pi \text{ in}^2
\]

2. **Determine the portion of the pie that was eaten**:
The family ate 5 out of 8 slices, which correspond to an angle of 225° (since \( 5/8 \) of 360° is \( 225° \)). To find out what fraction of the whole pie this represents:
\[
\text{Fraction eaten} = \frac{225°}{360°} = \frac{5}{8}
\]

3. **Calculate the area that was eaten**:
To find the area of the pie that was eaten, multiply the total area by the fraction eaten:
\[
\text{Area eaten} = \text{Total area} \times \text{Fraction eaten}
\]
\[
\text{Area eaten} = 25\pi \times \frac{5}{8}
\]
\[
\text{Area eaten} = \frac{125}{8}\pi
\]
\[
= 15.625\pi \text{ in}^2
\]

Therefore, the area of the pie that was eaten is:
\[
\boxed{15.625\pi \text{ in}^2}
\]