A semicircular window has diameter 63 cm. Find its perimeter (the curved edge plus the straight diameter).
Aptitude
Area
Difficulty: Easy
Choose an option
-
A162
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B132
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C142
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D172
Answer
Correct Answer: 162
Explanation
Introduction / Context:Perimeter of a semicircle consists of the semicircular arc plus the straight diameter edge. Recognizing this avoids the common mistake of using only the curved length.
Given Data / Assumptions:
- Diameter D = 63 cm.
- Radius r = D/2 = 31.5 cm.
- Perimeter P = arc length (half circumference) + diameter.
Concept / Approach:Full circumference is 2 * pi * r. Half of that is pi * r. Therefore P = pi * r + D. Using pi = 22/7 works neatly with multiples of 7.
Step-by-Step Solution:
r = 31.5 cm = 63/2 cmArc length = pi * r = (22/7) * (63/2) = (22 * 9) / 2 = 99 cmPerimeter P = arc + diameter = 99 + 63 = 162 cmVerification / Alternative check:Compute half circumference as (pi * D)/2 + D = (22/7 * 63)/2 + 63 = (198)/2 + 63 = 99 + 63 = 162 cm. Same result confirms consistency.
Why Other Options Are Wrong:
- 132, 142, 172: Each misses the exact arithmetic from using pi = 22/7 with D divisible by 7. 132 would be the half circumference only if r were 42, which it is not.
Common Pitfalls:
- Forgetting to add the diameter after computing the arc.
- Using 2 * pi * r instead of pi * r for the arc portion.
Final Answer:162