Problem

The central angles made by each slice of pizza listed in the following table: \begin{tabular}{|cc|} \hline Name & Central Angle ul Piza 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? \[ \begin{array}{l} 3.14159 \times 16=50.27 \text { inches } \\ 360 / 8=45 \text { degrees } \\ 45 / 360 \times 50.265=5.029=5.03 \text { inches } \end{array} \] 2. What is the area of John's slice?

Solution

Step 1 :Given that the diameter of the pizza is 16 inches, we can calculate the circumference of the pizza using the formula \(C = \pi d\), where \(d\) is the diameter. Substituting the given diameter, we get \(C = 3.14159 \times 16 = 50.27\) inches.

Step 2 :Next, we calculate the central angle of John's slice. Since the pizza is divided into 8 equal slices, each slice has a central angle of \(360 / 8 = 45\) degrees.

Step 3 :However, John's slice has a central angle of 36 degrees, which is less than the average slice. Therefore, the length of the crust of John's slice is \(36 / 360 \times 50.265 = 5.029\), which rounds to \(5.03\) inches.

Step 4 :To find the area of John's slice, we first calculate the area of the whole pizza using the formula \(A = \pi r^2\), where \(r\) is the radius of the pizza. Since the diameter is 16 inches, the radius is \(16 / 2 = 8\) inches. Substituting the radius into the formula, we get \(A = 3.14159 \times 8^2 = 201.06192982974676\) square inches.

Step 5 :Since John's slice represents \(36 / 360 = 1/10\) of the pizza, the area of John's slice is \(1/10 \times 201.06192982974676 = 20.106192982974676\) square inches.

Step 6 :Rounding to two decimal places, the area of John's slice is approximately \(\boxed{20.11}\) square inches.

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Source: https://solvelyapp.com/problems/19234/

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