Question

Dave ordered a large Domino's pizza. The large pizzas have a diameter of 15 inches. The delivery driver ended up eating part of the pizza on the way to Dave's house. The missing section forms an angle of 220 degrees. What is the area of the pizza that was eaten? Round your answer to the nearest tenth.



(1 point)
Responses

14.7 square inches
14.7 square inches

89.4 square inches
89.4 square inches

108.0 square inches
108.0 square inches

46.1 square inches

Answer 1

To find the area of the pizza that was eaten, we first need to determine the area of the entire pizza and then find the fraction of that area corresponding to the 220-degree angle the delivery driver ate.

1. **Calculate the area of the entire pizza:**
The area \( A \) of a circle is given by the formula:

\[
A = \pi r^2
\]

The radius \( r \) of the pizza is half of the diameter:

\[
r = \frac{15 \text{ inches}}{2} = 7.5 \text{ inches}
\]

Now, plug the radius into the area formula:

\[
A = \pi (7.5^2) = \pi (56.25) \approx 176.71 \text{ square inches}
\]

2. **Calculate the fraction of the pizza that was eaten:**
The pizza is a circle of 360 degrees, and the driver ate a section of 220 degrees. The fraction of the pizza eaten is:

\[
\text{Fraction eaten} = \frac{220}{360}
\]

Simplifying that:

\[
\frac{220}{360} = \frac{11}{18}
\]

3. **Find the area of the eaten section:**
The area of the eaten section is then:

\[
\text{Area eaten} = A \times \text{Fraction eaten} = 176.71 \times \frac{11}{18}
\]

Calculating that:

\[
\text{Area eaten} \approx 176.71 \times 0.6111 \approx 107.1 \text{ square inches}
\]

4. **Round to the nearest tenth:**

\[
\text{Area eaten} \approx 107.1 \text{ square inches}
\]

Looking at the options, the closest answer is **108.0 square inches**.

Final answer: **108.0 square inches**.