Question

find the length of an are of a circle of radius
10 cm, which subtends an angle 60° at the
centre.​

Answer 1

Given:-

• Radius ,r = 10 cm
• Angle ,∅ = 60°

To Find:-

• Length of arc , l

Solution:-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

It is given that the radius of circle is 10cm which subtends an angle 60° at the centre. we calculate the length of arc

Using formula to calculate the length of arc.

• l = ∅/360 × 2πr

where,

• l denote length of arc
• ∅ denote angle at the centre
• π denote 22/7
• r denote radius

Substitute the value we get

$:\implies$ l = 60/360 × 2×22/7 × 10

$:\implies$ l = 1/6 × 44/7 × 10

$:\implies$ l = 440/42

$:\implies$ l = 10.47 cm

• Hence, the length of the arc is 10.47 cm.

Answer 2

Answer:

Given :-

• A circle of radius is 10 cm, which subtends an angle of 60° at the centre.

To Find :-

• What is the length of an arc of a circle.

Formula Used :-

$\clubsuit$ Arc Length Formula :

$\longmapsto \sf\boxed{\bold{\pink{Arc\: Length =\: 2{\pi}r \bigg\lgroup \dfrac{\theta}{360}\bigg\rgroup}}}$

where,

• r = Radius of the circle
• $\theta$ = Central Angle of arc

Solution :-

Given :

$\bigstar$ Radius (r) = 10 cm

$\bigstar$ Central Angle of arc = 60°

According to the question by using the formula we get,

$\longrightarrow \sf Arc\: Length =\: 2 \times \dfrac{22}{7} \times 10 \times \bigg(\dfrac{60^{\circ}}{360}\bigg)$

$\longrightarrow \sf Arc\: Length =\: \dfrac{44}{7} \times 10 \times \bigg(\dfrac{60^{\circ}}{360}\bigg)$

$\longrightarrow \sf Arc\: Length =\: \dfrac{440}{7} \times \bigg(\dfrac{60^{\circ}}{360}\bigg)$

$\longrightarrow \sf Arc\: Length =\: \dfrac{2640\cancel{0}}{252\cancel{0}}$

$\longrightarrow\sf Arc\: Length =\: \dfrac{2640}{252}$

$\longrightarrow \sf\bold{\red{Arc\: Length =\: 10.47\: cm}}$

$\therefore$ The length of an arc of a circle of radius is 10.47 cm .