The radius of a certain circle is $30$ cm, Find the approximate length of arc if the length of the chord of the arc be $30$ cm.

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Solution

Let ABC be the circle whose centre is O and AC is chord. in $Δ$ AOC, $A O = O C = A C$ = $30$ cm,
$∵ ∠ A O C = 60^{\circ} = \frac{π}{3}$

Hence, arc AC = $\frac{∠ A O C}{360} \times 2 π \times r a d i u s$

= $r a d i u s \times \frac{π}{3} = 30 \times \frac{π}{3} = 10 π = 31.4159$ cm

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The radius of a certain circle is 30 cm, Find the approximate length of arc if the length of the chord of the arc be 30 cm.

Let ABC be the circle whose centre is O and AC is chord. in ΔAOC, AO=OC=AC=30 cm, ∵∠AOC=60∘=π3Hence, arc AC = ∠AOC360×2π×radius= radius×π3=30×π3=10π=31.4159 cm

The radius of a certain circle is $30$ cm, Find the approximate length of arc if the length of the chord of the arc be $30$ cm.

Let ABC be the circle whose centre is O and AC is chord. in $Δ$ AOC, $A O = O C = A C$ = $30$ cm,
$∵ ∠ A O C = 60^{\circ} = \frac{π}{3}$

Hence, arc AC = $\frac{∠ A O C}{360} \times 2 π \times r a d i u s$

= $r a d i u s \times \frac{π}{3} = 30 \times \frac{π}{3} = 10 π = 31.4159$ cm