Question

Q15 solve

​Q15. What is the angle subtended at the centre of a circle of radius 5 cm by an arc length 4 $\mathrm{\pi }$ cm .

Answer 1

Dear student,


$$\begin{gathered} Weknowthat, \\ Lengthofarc=\frac{\theta }{360°}\times 2\mathrm{\pi }r \\ \Rightarrow 4\cancel{\mathrm{\pi }}=\frac{\mathrm{\theta }}{360°}\times 2\times \cancel{\mathrm{\pi }}\times 5 \\ \Rightarrow 4=\frac{\mathrm{\theta }}{36\cancel{0}°}\times 1\cancel{0} \\ \Rightarrow 4\times 36=\mathrm{\theta } \\ \Rightarrow \boxed{\mathrm{\theta }=144°} \\ \mathrm{Thus}\mathrm{the}\mathrm{angle}\mathrm{subtended}\mathrm{at}\mathrm{the}\mathrm{centre}\mathrm{of}\mathrm{a}\mathrm{circle}\mathrm{of}\mathrm{radius}\mathrm{is}144° \end{gathered}$$
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