The area of a semicircle is 1925 square centimetres. What is the perimeter of the semicircle (in cm)? (Use π = 22/7.)

Introduction / Context:
This problem checks understanding of the relationship between the area and perimeter of a semicircle. It requires working backwards from the given area to find the radius, and then using that radius to compute the total boundary length, which includes both the curved part and the diameter. Such questions are common in aptitude exams and help reinforce how circle formulas are connected and how to correctly use π approximations such as 22/7 for calculation.

Given Data / Assumptions:
• Area of the semicircle is 1925 square centimetres.
• π is to be taken as 22/7.
• Let the radius of the semicircle be r centimetres.
• Perimeter of a semicircle consists of the curved arc plus the diameter, so it is πr + 2r.

Concept / Approach:
The area of a full circle is πr², so the area of a semicircle is (1/2) * πr². We are given this area and must solve for r. Once the radius is known, the perimeter of the semicircle is the sum of the curved length (half the circumference, which is πr) and the straight diameter (2r). The steps therefore involve rearranging the area formula, substituting π = 22/7, solving for r² and r, and then computing the perimeter expression.

Step-by-Step Solution:
Step 1: Use the semicircle area formula: (1/2) * π * r² = 1925. Step 2: Substitute π = 22/7 to get (1/2) * (22/7) * r² = 1925. Step 3: Simplify the constant factor: (1/2) * (22/7) = 11/7, so we have (11/7) * r² = 1925. Step 4: Rearrange for r²: r² = 1925 * (7/11) = 1925 * 7 / 11. Step 5: Compute the product: 1925 * 7 = 134, so we factor it carefully: 1925 / 11 = 175, so r² = 175 * 7 = 1225. Step 6: Hence r = √1225 = 35 centimetres. Step 7: Now compute the perimeter of the semicircle: P = πr + 2r = (22/7) * 35 + 2 * 35. Step 8: Evaluate the curved part: (22/7) * 35 = 22 * 5 = 110, and the diameter is 70, so total perimeter is 110 + 70 = 180 centimetres.

Verification / Alternative check:
We can quickly verify by plugging r = 35 back into the area formula. The area of the full circle would be πr² = (22/7) * 35². Here 35² = 1225, and (22/7) * 1225 = 22 * 175 = 3850. Since a semicircle is half of a full circle, its area is 3850 / 2 = 1925 square centimetres, which matches the given area. This confirms that r = 35 centimetres is correct. Once the radius is correct, the perimeter calculation πr + 2r is straightforward and leads to 180 centimetres, so the answer is consistent from both directions.

Why Other Options Are Wrong:
160 centimetres is too small and would correspond to a smaller radius than the one obtained from the given area, which would not satisfy the area condition.
200 and 220 centimetres are too large, implying a larger radius and therefore a larger area than 1925 square centimetres.
240 centimetres is significantly higher and clearly incompatible with the given area when checked with the semicircle formulas. Only 180 centimetres maintains consistency between area and perimeter.

Common Pitfalls:
A common mistake is to forget that the given area is for a semicircle, not a full circle, leading to missing the factor of 1/2. Another error is miscomputing with the fraction 22/7 and mixing up multiplication or division, especially when rearranging to solve for r². Some learners mistakenly calculate the perimeter as just πr or as 2πr, forgetting to add the diameter for a semicircle. Being systematic with formulas and carefully checking each arithmetic step helps avoid these issues.

Final Answer:
The perimeter of the semicircle is 180 centimetres.