Question

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

Options

• 10 cm

• 12 cm

• 14 cm

• 16 cm

Answer 1

We know that perimeter of a semi-circle of radius    `r=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=1/2(2pi r)+2r`

Multiplying both sides of the equation by 2 we get,

`72=2pir+4r`

Substituting `pi=22/7` we get,

`72=2xx22/7 r+4r`

`∴ 72=44/7 r+4r`

Now we will multiply both sides of the equation by 7.

`504=44r+28 r`

Adding like terms we get,

`∴ 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`

∴ Diameter=`2xx7`

∴ Diameter=`14`

Hence, diameter of the semi-circle is `14 cm`