Sector of a circle (pizza slice): A circular pizza of diameter 14 inches is cut into slices each subtending a central angle of 45°. Find the area of one slice (in square inches).

Introduction / Context:The area of a circular sector equals the corresponding fraction of the full circle’s area, with fraction = (central angle)/360°.

Given Data / Assumptions:

• Diameter = 14 in → radius r = 7 in.
• Central angle = 45°.

Concept / Approach:Full area = πr^2 = 49π. Sector area = (45/360) * 49π = (1/8) * 49π.

Step-by-Step Solution:

Verification / Alternative check:Eight equal slices would total back to 49π (~153.94), confirming each at ~19.24 in^2.

Why Other Options Are Wrong:16.25, 18.25, 17.25, 20.25 are not equal to 49π/8 when evaluated.

Common Pitfalls:Using diameter instead of radius in πr^2 or using 45/180 instead of 45/360 for the sector fraction.

Final Answer:19.25