Question

A cherry pie has a diameter of 9 in. If part of the cherry pie is eaten, the missing section forms an angle of 30°. What is the area of the cherry pie that was eaten? Round your answer to the nearest tenth. (1 point) Responses 21.2 in² 21.2 in² 5.3 in² 5.3 in² 42.4 in² 42.4 in² 4.7 in²

Answer 1

To find the area of the cherry pie that was eaten, we can use the formula for the area of a sector of a circle.

1. **Calculate the radius of the pie**:
The diameter of the pie is 9 inches, so the radius \( r \) is:
\[
r = \frac{9}{2} = 4.5 \text{ inches}
\]

2. **Calculate the area of the entire pie**:
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Substituting the radius:
\[
A = \pi (4.5)^2 = \pi \times 20.25 \approx 63.617 \text{ in}^2
\]

3. **Calculate the area of the sector**:
The area of the sector for a given angle \( \theta \) (in degrees) can be calculated using the following formula:
\[
\text{Area of sector} = \frac{\theta}{360} \times \text{Area of circle}
\]
Here, \( \theta = 30^\circ \):
\[
\text{Area of sector} = \frac{30}{360} \times 63.617 \approx \frac{1}{12} \times 63.617 \approx 5.3014 \text{ in}^2
\]

4. **Round to the nearest tenth**:
Rounding \( 5.3014 \) to the nearest tenth gives:
\[
\text{Area of the eaten pie} \approx 5.3 \text{ in}^2
\]

Thus, the area of the cherry pie that was eaten is **5.3 in²**.