In the given right-circular cone,
By applying pythagoras theorem, we get slant height(l),
l2 = 52 + 122
l = 13
Circumference(2πr) of the circle(i.e., the base of the right-circular cone) is the arc length of the sector of the circle(L)
L = 2πr
L = 10π
The slant height(l) of the right-circular cone is the Radius(R) of the sector of the circle
R = 13
The arc length(L) of the sector is given by:
L = θ × R
θ = LR
θ = 10π13
Therefore, θ = 10π13