Question

a wire of length 18cm is bend in the format a sector of length of arc 10cm. find the angle in radian and degree. subtended by the arc at the center of the circle.also find the area of the sector.is calculations​

Answer 1

Answer:

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Answer 2

The value of $\theta$ in radian = 2.5 radian

The value of $\theta$ in degree = 143.32 °

The area of the sector A = 20 $cm^{2}$

Step-by-step explanation:

From the figure

Length of the arc  BC = 10 cm

AB = BC = 4 cm

Angle subtended by the arc on the center =  $\theta$

Length of the arc is given by L = $\theta$ × r ------- (1)

⇒ 10 = $\theta$ × 4

⇒ $\theta$ = 2.5 radian

This is the value of $\theta$ in radian.

The value of angle $\theta$ in degree is   2.5 × $\frac{180}{\pi}$

⇒ $\theta$ = 143.32 °

This is the value of $\theta$ in degree.

Area of the sector

$A = \pi r^{2} \frac{\theta}{360}$

Where  $\theta$ is in degree.

Put all the values in above formula we get

$A = \pi 4^{2} \frac{143.32}{360}$

A = 20 $cm^{2}$

This is the area of the sector.