The radius of the sector formed from a cone

Question

A cone whose base diameter and vertical height are 24cm and 5cm respectively is unfolded to form a sector of a circle. Calculate

1) The radius of the sector

2) The angle of the sector

Answer 1

The height of the cone = 5 cm.

So the radius of the sector = √(24²+5²) = 24.51cm

To find the angle of the sector, we need the length of the arc of the sector.

Length of the arc(l) = perimeter of the circular base of the cone = 2πr

= 2π (24/2)

= 24π cm ≈ 75.40 cm

Now the angle = l/r [r = radius of the sector = 24.51 cm]

= 3.08 radians