A circular pizza that is 1212 inches in diameter is cut into 66 equal slices. What is the area of one of the​ slices?

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Part 1
The area of one slice is enter your response here in squaredin2.

1 answer

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 \(\boxed{5540.62} \text{ square inches}\).