Question

A circle of radius 120 m is divided into 8 equal sectors. Find the length of the arc of each of the sectors.​

Answer 1

$\huge\red{\fbox{SOLUTION:-}}$

see in the attachment

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Answer 2

Question:

• A circle of radius 120 m is divided into 8 equal sectors. Find the length of the arc of each of the sectors.​

Answer:

• The length of the arc is 30 π m

Explanation:

Given that:

• The radius of a circle is 120 m
• It is divided into 8 equal sectors

To Find:

• The length of the arc of each sector

Required Solution:

• Now let's find the angle made by the each segment

$\leadsto \;{\pink{\boxed{\bf{ Angle(\emptyset) = \dfrac{360}{No. of \; segments} }}}$  

Calculations :

$\longrightarrow \rm Central \; angle \; (\emptyset ) = \dfrac{360}{n}$

$\longrightarrow \rm Central \; angle \; (\emptyset ) = \dfrac{360}{8}$

$\longrightarrow {\red{\underline{\underline{\rm {Central \; angle \; (\emptyset ) =45^0}}}}}$

$\; \; \; \; \; \; {\underline{\pmb{\sf{ Henceforth , the \; measure \; of \; the \; central \; angle \; is \; 45 ^0 }}}}$

~ Now let's find the length of each of the arc

• Using formula to find the length of the arc

$\leadsto \; {\boxed{\bf{ Length \; of \; arc = \frac{\emptyset}{360^0} * 2\pi r}}}$

Calculations :

$\longrightarrow \rm Length \; of \; arc = \dfrac{\emptyset}{360^0} * 2\pi r$

$\longrightarrow \rm Length \; of \; arc = \dfrac{45^0}{360^0} * 2\pi (120m)$

$\longrightarrow \rm Length \; of \; arc = \dfrac{1}{8} * 2*\pi * 120\; m$

$\longrightarrow \rm Length \; of \; arc = 2* \pi * 15 \; m$

$\longrightarrow {\red{\underline{\underline{\rm {Length \; of \; arc\; =30 \pi \; m }}}}}$

$\; \; \; \; \; \; {\underline{\pmb{\sf{ Henceforth , the \; measure \; of \; the \; arc \; is \; 30 \pi \; m}}}}$

Therefore:

• The measure of each of the arc of the circle is 30π m

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