Question

a sector of a circle has an angle of 30° if the sector has a radius of 24 cm what is the length of the arc?
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Answer 1

Answer:

Radius of circle= 24 cm

Angle of sector = 30°

Now,

Length of Arc= 30°÷360×2πr

=30°÷360°×2×22/7×24

=88/7cm

Answer 2

Given :

• Angle = 30°.

• Radius = 24 cm.

To find :

Length of the arc.

Solution :

We know the formula for length of an arc i.e,

$\boxed{\bf{s = 2\pi r \times \dfrac{\theta}{360^{\circ}}}}$

Where :

• s = Length of the arc.
• r = Radius

By using the above formula and substituting the values in it, we get :.

$:\implies \bf{s = 2 \times \dfrac{22}{7} \times 24 \times \dfrac{30^{\circ}}{360^{\circ}}}$

$:\implies \bf{s = 2 \times \dfrac{22}{7} \times 24 \times \dfrac{1}{12}}$

$:\implies \bf{s = \dfrac{22}{7} \times 24 \times \dfrac{1}{6}}$

$:\implies \bf{s = \dfrac{22}{7} \times 4}$

$:\implies \bf{s = \dfrac{88}{7}}$

$:\implies \bf{s = 12.6}$

$\boxed{\therefore \bf{s = 12.6}}$

Hence the arc length is 12.6 cm.