If the perimeter of a semi-circular protractor is $36\text{ cm}$, then its diameter is:
(a) $14\text{ cm}$
(b) $7\text{ cm}$
(c) $28\text{ cm}$
(d) $21\text{ cm}$
Step-by-Step Solution
Key Concept: Perimeter of semi-circle $= \pi r + 2r = r(\pi + 2) = 36$.
$r\left(\dfrac{22}{7} + 2\right) = r\left(\dfrac{36}{7}\right) = 36 \Rightarrow r = 7\text{ cm}$. [0.5 Mark]
Diameter $= 2r = 14\text{ cm}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Applying semi-circle perimeter formula: 0.5 Mark
Calculating diameter $= 14\text{ cm}$: 0.5 Mark
Correct Answer: $14\text{ cm}$