Perimeter of a semicircle (radius = 28 cm)\nFind the perimeter of a semicircle of radius 28 cm (use perimeter = πr + 2r).

Difficulty: Easy

Correct Answer: 144

Explanation:


Introduction / Context:
The boundary length of a semicircle includes the curved arc plus the diameter. The standard formula is Perimeter = (1/2 of circumference) + diameter = πr + 2r.


Given Data / Assumptions:

  • Radius r = 28 cm
  • Use π = 22/7 for exact integer outcomes.


Concept / Approach:
Compute the arc component πr and add the straight diameter 2r. Avoid using the full circumference 2πr, since we only have half the circle plus the diameter.


Step-by-Step Solution:

Arc (semicircle) = πr = (22/7) * 28 = 88 cm Diameter = 2r = 56 cm Perimeter = 88 + 56 = 144 cm


Verification / Alternative check:
Using π ≈ 3.14 gives 3.14*28 + 56 ≈ 87.92 + 56 ≈ 143.92, rounding to 144, consistent with exact form.


Why Other Options Are Wrong:
288 doubles the arc; 121 and 242 are unrelated to πr + 2r with r = 28 cm; only 144 matches.


Common Pitfalls:
Forgetting to include the diameter or mistakenly halving 2πr to πr and then halving again causes errors.


Final Answer:
144

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