Question

a wire of length 44cm is bent into an arc of a circle radius 12cm the angle (in dress)subtended by the arc at the centre of the circle is pls solve this urgent​

Answer 1

Step-by-step explanation:

Given :-

A wire of length 44cm is bent into an arc of a circle radius 12cm.

To find :-

Find the angle subtended by the arc at the centre of the circle ?

Solution :-

Let the angle subtended by the arc at the centre of the circle be X°

Given that

Length of the wire = 44 cm

If it is bent into an arc of a circle

Length of the arc = 44cm

Given that

Radius = 12 cm

We know that

The length of the arc = (X°/360°)×2πr

=> (X°/360°)×2πr = 44

=> (X°/360°)×2(22/7)×(12) = 44

=> (X°×2×22×12)/(360°×7) = 44

=>(X°×44×12)/(360°×7) = 44

=> 12X°/(360°×7) = 44/44

=> 12X°/360°×7 = 1

=>X°/(30×7) = 1

=> X° /210 = 1

=>X° = 210×1

=> X° = 210°

The angle = 210°

Answer:-

The angle subtended by the arc at the centre of the circle is 210°

Check :-

The angle = 210°

Radius = 12 cm

Length of the arc = (X°/360°)×2πr

=> (210/360)×2×(22/7)×12

=> (210×2×22×12)/(360×7)

=> 440/10

=> 44

Length of the arc = 44 cm

The length of the arc = 44 cm

Verified the given relations in the given problem

Used formulae:-

• Length of the arc = (X°/360°)×2πr

Where,

• r = radius of the circle

• X° = The angle subtended by the arc at the centre of the circle

• l = length of the arc

Answer 2

Have Given :-

$wire \: \: length = 44cm$

$circumference = 2\pi r$

$2\pi r = 44$

$\pi r = \frac{44}{2}$

$\pi r = 22$

$r = \frac{22}{\pi}$

$arc \: \: radius = 12cm$

$angle \: subtended \: \theta = \frac{arc \: length}{radius}$

$= \frac{44}{12}$

$= \frac{11}{3}$

$\scriptsize \theta = \frac{11}{ \cancel3} \times \frac{ \cancel{180}}{\pi} \: ( \because1 \: radian = \frac{180°}{\pi})$

$\theta = \frac{11 \times 60}{\pi}$

$\theta = ( \frac{660}{\pi} )°$

I hope it is helpful