Question

In a circle , find the length of a 90 arc if an inscribed regular hexagon has a side of length 12 cm. Give only the number (no units), and round your answer to the hundredths place.

Answer 1

18.85

Explanation:

The relation between a circle and an inscribed hexagon is that the radius of the circle is equal the side of the hexagon. So as the length of the side is 12 cm, we have that the radius is 12 cm.

Now we can solve to find the length of a 90 arc with a rule of three:

360 arc -> 2*pi*r cm

90 arc -> x cm

2*pi*12 / x = 360 / 90

24pi / x = 4

4x = 24pi

x = 6pi = 18.8496

rounding to nearest hundredth, we have x = 18.85