A cone is formed from a sector of a circular of radius 9cm which sustained an angel 120 find (a) the radius of the cone formed (b) the curved surface area of the cone (c) the total surface (d) volume

Answer 1

I used to illustrate this problem to my students by taking a cone-shaped drinking cup from a water dispenser and cutting it open to show just that kind of a sector.
It was easy to see that the arc of that sector becomes the circular base of the cone, so ....

since the angle is 120°, the arc length would be 1/3 of the circumference
(1/3)(2π)(9) cm = 6π cm
- this is the circumference of the base of the cone, and the slant height of the cone would be 9 cm
radius of cone ---- r
2πr = 6π
r = 3 cm
height^2 + 3^2 = 9^2
height^2 = 72
height = √72 = 6√2 cm

surface area of cone = πrs
= π(3)(9) = 27π cm^2

V = (1/3)π r^2
= (1/3)π(81) = 27π cm^3

check my arithmetic