Question

If an arc forms 72 degree at the centre of the circle, then the ratio of its length to circumference of circle is:

Answer 1

total circumference = 2πr

length of arc=$\frac{72}{360}$×2πr

so, ratio of its length to circumference of the circle is

$=\frac{\frac{72}{360} * 2\pi r }{2\pi r} \\=\frac{\frac{1}{5} * 2\pi r }{2\pi r }\\ =\frac{1}{5}$

So, the ratio is 1:5

Answer 2

Step-by-step explanation:

total circumference = 2πr

length of arc=\begin{gathered}\frac{72}{360} \\\end{gathered}

360

72

×2πr

so, ratio of its length to circumference of the circle is

\begin{gathered}=\frac{\frac{72}{360} * 2\pi r }{2\pi r} \\=\frac{\frac{1}{5} * 2\pi r }{2\pi r }\\ =\frac{1}{5}\end{gathered}

=

2πr

360

72

∗2πr

=

2πr

5

1

∗2πr

=

5

1