If the perimeter of a semi-circular protractor is 36 cm, then its diameter is

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KollegeApply · Accepted Answer

We know that perimeter of a semi-circle of radius r=$\frac{1}{2}$(2pir)+2r.................(1) We have given the perimeter of the semi-circle and we are asked to find the diameter of the semi-circle. Therefore, substituting the perimeter of the semi-circle in equation (1) we get, 36=$\frac{1}{2}$(2pi r)+2r Multiplying both sides of the equation by 2 we get, 72=2pir+4r Substituting pi=$\frac{22}{7}$ we get, 72=2xx22/7 r+4r $\therefore$ 72=$\frac{44}{7}$ r+4r Now we will multiply both sides of the equation by 7. 504=44r+28 r Adding like terms we get, $\therefore$ 504=72 r Dividing both sides of the equation 72 we get, r=7 Therefore, radius of the semi circle is 7cm. Now we will find the diameter. Diameter=2xxr $\therefore$ Diameter=2xx7 $\therefore$ Diameter=14 Hence, diameter of the semi-circle is 14 cm

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