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If the perimeter of a semicircular protractor is $36 cm$ ; its diameter is

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12 cm

14 cm

18 cm

16 cm

answer is A.

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Detailed Solution

Given that, the perimeter of a semicircular protractor is

36 cm

.
Let r represents the radius of the protractor.
Determining the value of r by using the formula for perimeter of semicircle.

P = 12 2 π r + 2 r

⇒

36 = 12 2 π r + 2 r

⇒

72 = 2 π r + 4 r

Substitute

227 for π

into the equation and solve for r.

72 = 2227 r + 4 r

⇒

72 = 447 r + 4 r

⇒

504 = 44 r + 28 r

⇒

504 = 72 r

⇒

r = 7

The diameter of a circle is double its radius so perform multiplication between 7 and 2.
D = 7

×

⇒

D = 14
Therefore, the diameter of the circle is represented by 14 cm.
Hence the correct option is 1.

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