Question

A piece of wire of length 108 cm is bent to form
a semicircular arc bounded by its diameter.
Find its radius and enclosed area.
​

Answer 1

$\huge\tt\pink{Answer}$

Length of wire = 108 cm

Let r be the radius of the semicircle

πr+ 2r = 108

⇒ r(π + 2) = 108 ⇒ r = ((22/7) + 2) =  108

⇒ (36/7)r = 108  ⇒ r = (108 × 7)/36 = 27 cm

Area = πr2 /2 = (22/(7 × 2)) × 21 × 21 = (1386/2) cm2

= 693 cm2

$\huge\tt\pink{thnks}$

Answer 2

Given:

Length of the wire - 108 cm .

To find :

Radius and enclosed area?

Solution :

Length of the wire = 108 cm .

Let x be the radius of the semicircle.

πr+ 2r = 108

$= > r \: (\pi + 2) = 108 = r = (( \frac{22}{7} ) + 2 = 108$

$= > ( \frac{36}{7} ) \: r = 108 = r = \frac{(108 \times 7)}{36} = 27 \: cm.$

Area,

$= > \frac{\pi \: r {}^{2} }{2}$

= (22/(7 × 2)) × 21 × 21 = (1386/2) cm2

= 693 cm².