Question

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





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Answer 1

Question:

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

Answer:

• Length of arc is 27.5 cm (approx).

Step-by-step Explanation:

Given:

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

To Find:

• Length of arc of a circle?

Required Formula:

${\color{orange}\bigstar}\:{\underline{\boxed{\frak{Length\:of\:arc = \dfrac{\theta}{360}\:\times\:2\pi r}}}}$

Where,

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

We have,

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

Solution:

$\begin{gathered} \begin{gathered} \underline{ \underline{\pmb {\frak{ \color{red}{According \: to \: the \: question}}}}}\\ \\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{\theta}{360}\:\times\:2\pi r\end{gathered} \\ \\ \underline{ \frak \color{navy}{Putting \: all \: values \: in \: the \: formula \: we \: get,}} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{\cancel{105}}{360}\:\times\:2\:\times\:\dfrac{22}{\cancel{7}}\:\times\:15\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = {\cancel{\dfrac{15}{360}}}\:\times\:2\:\times\:22\:\times\:15\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{1}{\cancel{24}}\:\times\:\cancel{44}\:\times\:15\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{1}{6}\:\times\:11\:\times\:15\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{11\:\times\:15}{6}\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\sf Length\:of\:arc = \dfrac{165}{6}\end{gathered} \\ \\ \begin{gathered}\\ \hookrightarrow\:\underline{\boxed{\frak{Length\:of\:arc\:\approx\:27.5\:cm \: approx. \: }}} \orange\bigstar\end{gathered}\end{gathered} \\ \\ \\ \underline{\sf{Hence, length \: of \: the \: arc \: is  \textsf{\textbf{27.5 cm (approx)}}}.}$

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