A circular pizza has a diameter of 14 inches. A slice is cut such that the slice corresponds to a central angle of 45°. What is the area of each slice of pizza (in square inches)?

Introduction / Context:
This question involves finding the area of a sector of a circle, representing a slice of pizza. The central angle of the slice and the diameter of the pizza are given. This type of problem is common in aptitude and quantitative exams to test understanding of circular geometry, especially the relation between the area of a full circle and the area of a sector based on its central angle.

Given Data / Assumptions:

• Diameter of the pizza = 14 inches, so radius r = 14 / 2 = 7 inches.
• Central angle of each slice = 45°.
• The pizza is a perfect circle.
• We may use π ≈ 3.14 for numerical calculation.
• We are required to calculate the area of one slice, which is the area of a 45° sector.

Concept / Approach:
The area of a circle is A = π * r^2. A sector with central angle θ degrees has area equal to (θ / 360) times the area of the full circle. Therefore, if we know the radius and the central angle, we can first compute the total area of the pizza and then multiply by the fraction θ / 360. This method directly provides the area of a single slice.

Step-by-Step Solution:
Radius r = 7 inches.Area of full pizza = π * r^2 ≈ 3.14 * 7^2 = 3.14 * 49.Compute 3.14 * 49 ≈ 153.86 square inches.Each slice corresponds to a central angle of 45°, so fraction of circle = 45 / 360 = 1 / 8.Area of one slice = (1 / 8) * 153.86 ≈ 19.23, which rounds to about 19.25 square inches.

Verification / Alternative check:
We can divide the circle area by 8 directly because 360° / 45° = 8 slices. If the total area is 49π, then area of each slice is (49π / 8). Taking π as 3.14, we get (49 * 3.14) / 8 ≈ 153.86 / 8 ≈ 19.23. Both calculation paths agree closely, and rounding to two decimal places gives approximately 19.25 square inches, which matches the chosen option.

Why Other Options Are Wrong:
Option 16.25 is significantly smaller and would correspond to a central angle less than 45°. Option 18.25 is slightly low and likely results from using π ≈ 3 instead of 3.14. Option 20.25 is higher than the correct sector area and overestimates the fraction. Option 17.25 is again too small and does not match any reasonable combination of radius and angle for this pizza.

Common Pitfalls:
Students often forget to convert the fraction of the circle by using θ / 360, instead using 45 / 180 or another incorrect ratio. Others may forget to square the radius or miscalculate 7^2. Some also use an overly rough approximation for π, which can shift the answer away from the correct option. Ensuring careful multiplication and division is essential for accuracy.

Final Answer:
The area of each slice of the pizza is approximately 19.25 square inches.