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