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 (approx)

(2 Points)

6.3cm

5.8cm

6.1cm

6.8cm

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Answer 1

Given:

Area of a sector of central angle 120° of a circle is 3π cm².

To find:

The length of the corresponding arc of this sector is (approx)

Solution:

Finding the radius of the circle:

The central angle, θ = 120°

The area of a sector of a circle, A = 3π cm²

We know,

$\boxed{\bold{Area \:of \: a \:sector = \frac{\theta }{360\° } \times \pi r^2 }}$

On substituting the values in the above formula, we have

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

$\implies 3 = \frac{120\° }{360\° } \times r^2$

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

$\implies r^2 = 3 \times 3$

$\implies \bold{r = 3 \:cm}$

Finding the arc length:

We know,

$\boxed{\bold{Arc \:Length= \frac{\theta }{360\° } \times 2\pi r}}$

On substituting the values in the above formula, we have

$Arc\:Length = \frac{120\° }{360\° } \times 2 \times \frac{22}{7} \times 3 }}$

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

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

$\implies \bold{ Arc\:Length = 6.28\:cm}$ ≈ $\bold{6.3\:cm}$

Thus, the length of the corresponding arc of this sector is (approximately) → option (1) → 6.3 cm.

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