Question

The arc length of a circle having radius 15 cm and subtending an angle 105 degree at the centre of circles is

Answer 1

Answer:

The arc length of the circle is 27.48 cm.

Step-by-step-explanation:

We have given that,

• Radius of circle ( r ) = 15 cm
• Angle subtended ( θ ) = 105°

We have to find the arc length of the circle.

We know that,

$\displaystyle{\pink{\sf\:Arc\:length\:=\:\dfrac{\theta}{360}\:\times\:2\:\pi\:r}}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:\dfrac{\cancel{105}}{\cancel{360}}\:\times\:2\:\times\:3.14\:\times\:15}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:\dfrac{\cancel{35}}{\cancel{120}}\:\times\:30\:\times\:3.14}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:\dfrac{7}{\cancel{24}}\:\times\:\cancel{30}\:\times\:3.14}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:\dfrac{7}{4}\:\times\:5\:\times\:3.14}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:1.75\:\times\:5\:\times\:3.14}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:5.495\:\times\:5}$

$\displaystyle{\implies\sf\:Arc\:length\:=\:27.475}$

$\displaystyle{\implies\underline{\boxed{\red{{\sf\:Arc\:length\:\approx\:27.48\:cm\:}}}}}$

∴ The arc length of the circle is 27.48 cm.

Answer 2

Question:

• The arc length of a circle having radius 15 cm and subtending an angle 105° at the centre of circles is?

Answer:

• Length of arc is 27.5 cm (approx).

EXPLANATION :

$\LARGE{\underline{\underline{\text{Given\::-}}}}$

• Radius of circle (r) = 15 cm
• Angle at the centre of circle (θ) = 105°

$\LARGE{\underline{\underline{\text{To\:Find\::-}}}}$

• Length of arc of a circle?

$\LARGE{\underline{\underline{\text{Formula\:Used\::-}}}}$

$\quad\star\:{\underline{\boxed{\frak{Length\:of\:arc = \dfrac{\theta}{360}\:\times\:2\pi r}}}}$

Where,

• θ denotes angle at centre
• π denotes pi
• r denotes radius of circle

We have,

• Angle at centre (θ) = 105°
• Pi (π) = 22/7
• Radius of circle (r) = 15 cm

$\LARGE{\underline{\underline{\text{Solution\::-}}}}$

According to the question,

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{\theta}{360}\:\times\:2\pi r$

Putting all values in the formula we get,

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{\cancel{105}}{360}\:\times\:2\:\times\:\dfrac{22}{\cancel{7}}\:\times\:15$

$\\ \hookrightarrow\:\sf Length\:of\:arc = {\cancel{\dfrac{15}{360}}}\:\times\:2\:\times\:22\:\times\:15$

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{1}{\cancel{24}}\:\times\:\cancel{44}\:\times\:15$

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{1}{6}\:\times\:11\:\times\:15$

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{11\:\times\:15}{6}$

$\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{165}{6}$

$\\ \hookrightarrow\:\underline{\boxed{\bf{Length\:of\:arc\:\approx\:27.5\:cm}}}\:\bigstar$

Hence, length of arc is 27.5 cm (approx).

EXTRA INFORMATION :

↠ Area of minor sector

ㅤㅤㅤㅤㅤ= θ/360 × πr²

↠ Area of major sector

ㅤㅤㅤㅤㅤ= πr² - Area of minor sector

↠ Area of minor segment

ㅤㅤㅤㅤㅤ= Area of corresponding sector- Area of corresponding ∆

↠ Area of major segment

ㅤㅤㅤㅤㅤ= πr² - Area of minor segment ↠ Length of arc of a sector

ㅤㅤㅤㅤㅤ= θ/360 × 2πr

↠ Area of circle

ㅤㅤㅤㅤㅤ= πr²

↠ Circumference of circle

ㅤㅤㅤㅤㅤ= 2πr

$\red{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\purple{\rule{45pt}{7pt}}$