Find the perimeter (in cm) of a semicircle whose radius is 14 cm. Include both the curved arc and the diameter.

Introduction / Context:
This question asks for the perimeter of a semicircle when the radius is known. The perimeter of a semicircle consists of two parts: the curved half circumference and the straight diameter. Knowing how to combine these correctly is a basic but important skill in mensuration.

Given Data / Assumptions:

• Radius r of the semicircle is 14 cm.
• We must find the total perimeter: curved arc length plus the diameter.
• We use π = 22 / 7 for calculations.
• Full circumference of a circle is 2πr; half of this gives the semicircular arc.

Concept / Approach:
The perimeter P of a semicircle is given by: P = (1 / 2) * (2πr) + 2r = πr + 2r The term πr is the length of the curved arc (half the full circumference) and 2r is the diameter. We simply substitute the given radius into this formula and compute the numerical value using the chosen approximation for π.

Step-by-Step Solution:
Step 1: Write the perimeter formula for a semicircle: P = πr + 2r. Step 2: Substitute r = 14 cm. Step 3: Compute πr with π = 22 / 7: πr = (22 / 7) * 14 = 22 * 2 = 44 cm. Step 4: Compute the diameter: 2r = 2 * 14 = 28 cm. Step 5: Add to get total perimeter: P = 44 + 28 = 72 cm. Step 6: Therefore, the perimeter of the semicircle is 72 cm.

Verification / Alternative check:
We can cross check by first computing the full circumference and then halving it. Full circumference is 2πr = 2 * (22 / 7) * 14 = 2 * 44 = 88 cm. Half of that is 44 cm, which matches the curved part we used above. Adding the diameter 28 cm again gives 44 + 28 = 72 cm, confirming the perimeter is correct.

Why Other Options Are Wrong:
46 cm and 56 cm are too small and would result from forgetting part of the perimeter, such as using only the arc or only the diameter. 92 cm is larger than the full circumference of the circle and comes from adding 2πr and 2r rather than half the circumference. 144 cm is far too large and does not correspond to any simple misapplication of the formula with radius 14 cm, so it is inconsistent with the given dimensions.

Common Pitfalls:
A common error is to use only πr (curved part) and forget the diameter, or mistakenly use 2πr for the arc of the semicircle. Another pitfall is mixing units or approximations for π without tracking them carefully. Always remember that a semicircle's perimeter is πr plus 2r, not just the curved portion, and double check arithmetic when substituting the radius.

Final Answer:
The perimeter of the semicircle is 72 cm.