Module 10: Circles
Topic 4 Application: Arc Length and Area of a Sector Problem Set
You and five friends decide to go out and share a pizza for dinner. As a group, you select a pizza with a diameter of 16 inches. In this assignment, use the information below to determine each person's crust size and the size of each slice of pizza. Each person is only going to have one slice of pizza. Answer all of the questions in the blank spaces provided making sure to show all of your work. Round your answers to the nearest hundredth.
The central angles made by each slice of pizza listed in the following table:
\begin{tabular}{|cc|}
\hline Name & Central Angle of Pizza Slice \\
\hline John & $36^{\circ}$ \\
\hline Susan & $45^{\circ}$ \\
\hline Ashley & $70^{\circ}$ \\
\hline Kevin & $90^{\circ}$ \\
\hline Amy & $80^{\circ}$ \\
\hline Lisa & $29^{\circ}$ \\
\hline
\end{tabular}
1. What is the length of the crust in John's slice?
Answer
Final Answer: The length of the crust in John's slice is approximately \(\boxed{5.03}\) inches.
Step 1 ：The length of the crust in John's slice is the same as the length of the arc subtended by the central angle of his slice. The formula for the length of an arc is given by: \[\text{Arc length} = \frac{\text{Central angle}}{360} \times \text{Circumference of the circle}\]
Step 2 ：The circumference of a circle is given by: \[\text{Circumference} = \pi \times \text{Diameter}\]
Step 3 ：Given that the diameter of the pizza is 16 inches, we can substitute this into the formula for the circumference to get the circumference of the pizza.
Step 4 ：Then, we can substitute the central angle of John's slice and the circumference of the pizza into the formula for the arc length to get the length of the crust in John's slice.
Step 5 ：Final Answer: The length of the crust in John's slice is approximately \(\boxed{5.03}\) inches.
