Question

A circular pizza that is 1212 inches in diameter is cut into 66 equal slices. What is the area of one of the​ slices?
Question content area bottom
Part 1
The area of one slice is enter your response here in squaredin2.

Answer 1

To find the area of one slice of pizza, we can follow these steps:

1. **Calculate the radius of the pizza.**
The diameter is given as 1212 inches, so the radius \( r \) is half of that:
\[
r = \frac{1212}{2} = 606 \text{ inches}
\]

2. **Calculate the area of the whole pizza.**
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
Substituting the radius:
\[
A = \pi (606)^2
\]
Calculating \( 606^2 \):
\[
606^2 = 367236
\]
Therefore,
\[
A = \pi \times 367236 \approx 1150.79 \times 367236 \approx 1150.79 \times 3.14159 \approx 1150.79 \times 3.14159 \approx 1150.79 \approx 1150.79 \approx 367,236\pi \text{ square inches (using } \pi \approx 3.14159)
\]

3. **Calculate the area of one slice.**
Since the pizza is cut into 66 equal slices, the area of one slice \( A_{slice} \) is:
\[
A_{slice} = \frac{A}{66} = \frac{367236\pi}{66}
\]
Now, let's calculate that:
\[
A_{slice} \approx \frac{367236 \times 3.14159}{66} \approx \frac{1150.79}{66} \approx 5567.22 \text{ square inches}
\]
Therefore, the area of one slice is approximately:
\[
\frac{367236 \pi}{66} \approx 5540.62 \text{ square inches}
\]

Thus, the area of one slice is approximately \(\boxed{5540.62} \text{ square inches}\).