Question

What is the angle subtended in a circle at centre if it's radius is 6cm and the length of the arc is 3πcm(explanation needed)

Answer 1

L=3pie
r=6cm
angle subtended at the centre = L/r =3pie/6 =pie/2= 90°..... so the angle subtended is 90°at the centre.

Answer 2

method1:-
you know circumferrence of circle=2πr
=2π(3)=12π cm
we know 2πr(12π cm) circumference subtain 360°
hence ,
2πr=============360°

so, 1================360/2πr
so, 3π================{360/12π} x3π
=90°
hence 90 subtain in center by arc 3π cm

method2;-
we know formula
@=l/r
where @ is angle subtain in center
l is length of arc
r is radius
now,
@=3π/6=π/2
hence @=90°