Question

Area of a sector of central angle 120° of a circle is 3π cm2. Then the length of the corresponding arc of this sector is

Answer 1

Step-by-step explanation:

given angle is 120 and area is 3π

we know area of a sector is

Area = π r ^2 (C/360)

=> 3π=π * r^2 *(120/360)

=>r^2=9

so r will be 3

so the length of arc is 3cm

Answer 2

Answer:

The length of the corresponding arc of the sector is 6.3cm

Step-by-step explanation:

Given:

The area of a sector of central angle 120° of a circle exists at 3π cm².

To find:

The length of the corresponding arc of this sector exists (approx.)

Solution:

Finding the radius of the circle:

The central angle, $\theta=120^{\circ}$

The area of a sector of a circle, $A=3 \pi \mathrm{cm}^{2}$

Area of a sector $=\frac{\theta}{360^{\circ}} \times \pi r^{2}$

On substituting the values in the above equation, we have

$&3 \pi=\frac{120^{\circ}}{360^{\circ}} \times \pi r^{2}$

$&\Longrightarrow 3=\frac{120^{\circ}}{360^{\circ}} \times r^{2}$

$&\Longrightarrow 3=\frac{1}{3} \times r^{2}$

$&\Longrightarrow r^{2}=3 \times 3$

$&\Longrightarrow \mathbf{r}=\mathbf{3} \mathbf{c m}$

Finding the arc length:

Arc Length $=\frac{\theta}{360^{\circ}} \times 2 \pi \mathrm{r}$

By substituting the values in the above formula, we have

Arc Length $=\frac{120^{\circ}}{360^{\circ}} \times 2 \times \frac{22}{7} \times 3$

Arc Length $=\frac{1}{3} \times 2 \times \frac{22}{7} \times 3$

Arc Length $=2 \times \frac{22}{7}$

Arc Length $=6.28 \mathrm{~cm}=6.3 \mathrm{~cm}$

Hence, the length of the corresponding arc of the sector is 6.3cm

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