 # If the perimeter of a semi-circular Question:

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

(a) 10 cm

(b) 12 cm

(c) 14 cm

(d) 16 cm

Solution:

We know that perimeter of a semi-circle of radius $r=\frac{1}{2}(2 \pi r)+2 r$......(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,

$36=\frac{1}{2}(2 \pi r)+2 r$

Multiplying both sides of the equation by 2 we get,

$72=2 \pi r+4 r$

Substituting $\pi=\frac{22}{7}$ we get,

$72=2 \times \frac{22}{7} r+4 r$

$\therefore 72=\frac{44}{7} r+4 r$

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

$504=44 r+28 r$

$\therefore 504=72 r$

Dividing both sides of the equation 72 we get, $r=7$

Therefore, radius of the semi circle is $7 \mathrm{~cm}$.

Now we will find the diameter.

Diameter $=2 \times r$

$\therefore$ Diameter $=2 \times 7$

$\therefore$ Diameter $=14$

Hence, diameter of the semi-circle is $14 \mathrm{~cm}$.

Therefore, the correct answer is (c).