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).
Aptitude
Area
Difficulty: Easy
Choose an option
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A16.25
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B19.25
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C18.25
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D17.25
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E20.25
Answer
Correct Answer: 19.25
Explanation
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:
Area(slice) = (1/8) * 49π = 49π / 8.Using π ≈ 3.1416 → 49π/8 ≈ 153.938/8 ≈ 19.242 ≈ 19.25.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