DSSSB 6 September 2024
Non Nursing Subjects
Hard
The perimeter of a semicircular field is 180 cm. What is the diameter of the semicircle? [use pi = 22/7]
Appeared in: DSSSB 6 September 2024
Explanation
- The perimeter of a semicircle is the sum of its curved arc (πr) and its straight diameter (2r).
- The formula can be simplified to Perimeter = r(π + 2).
- Given the perimeter is 180 cm and π is 22/7, the equation is 180 = r(22/7 + 2), which simplifies to 180 = r(36/7).
- Solving for the radius (r) gives r = (180 * 7) / 36, which equals 35 cm.
- The diameter is twice the radius (d = 2r), so the diameter is 2 * 35 = 70 cm.
Why Other Options Were Wrong
- Option A: This value represents the radius of the semicircle, which is half of the diameter.
- Option B: This is an incorrect calculation that does not follow the correct formula for the perimeter of a semicircle.
- Option C: This value is a result of an incorrect calculation, likely from dividing the perimeter (180) by π (approximately 3.14), which would be 180 / (22/7) ≈ 57.27. This approach incorrectly ignores the diameter component of the perimeter.
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the diameter of a semicircle from its perimeter as background academic context rather than a clinical decision trigger.
- This question tests fundamental mathematical and problem-solving skills.
- While not directly clinical, proficiency in basic calculations is essential for tasks such as medication dosage calculation, fluid balance monitoring, and interpreting various medical scales and measurements.
- What if the question asked for the area? The area of a semicircle is (πr²)/2. With r = 35 cm, the area would be (22/7 * 35 * 35) / 2 = 1925 cm².
How to Approach the Question
- First, identify the geometric shape in the question, which is a semicircle.
- Recall the formula for the perimeter of a semicircle. Remember that the perimeter includes both the curved part (half the circumference of a circle) and the straight part (the diameter).
- The formula is: Perimeter = (π × radius) + (2 × radius) or P = r(π + 2).
- Substitute the given values into the formula: 180 for the perimeter and 22/7 for π.
- Solve the resulting equation for the radius (r).
- Once you find the radius, calculate the diameter by multiplying the radius by 2 (d = 2r).
Concept Tested & Keywords
- Concept Tested: Calculating the diameter of a semicircle from its perimeter.
- Stem keywords: perimeter, semicircular field, diameter
- Lead-in keywords: What is
Question ID
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Practise the full DSSSB 6 September 2024
Attempt every question from this paper in a timed mock, then review the full solution for each one.
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