Question

If the diameter of a semicircular protractor is 42 cm then find its perimeter

Answer 1

Perimeter of a circle  ( Circumference )= 2 * π * radius = 2πr

So, perimeter of semi circle ( half  the circle) = Half the perimeter = 2πr/2 = πr

Diameter = 2* radius

So, 42cm = 2 * radius

Therefore, radius = 42/2 = 21 cm

π has a value of 22/7 OR 3.14; Taking it to be 22/7 here

πr      ( π * radius )     = 22/7 * 21 = 22 * 3 = 66 cm

Answer : Perimeter of the semi circle/ Circumference of the semi circle is of       66 cm

(Note : As the value of π is not definite, and thus, not exactly 3.14 or 22/7 to calculate, but approximated to this value. Therefore, the answer of Circumference obtained here, is not an exact answer, and thus, may differ by some minute value if calculated using 3.14. WHere the answer would result as 65.94 . However, overall this answer is correct. )

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Answer 2

Perimeter of semicircle = πr + 2r

Since diameter= 42cm

Radius = diameter/2

= 42/2cm

= 21cm

Perimeter= 22/7 × 21cm + 2*21cm

= 462/7+42

=66+42

=108cm

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