# a sector is bent to form a cone. if the angle of the sector is 30 degrees and the radius is 6cm, what is the altitude of the cone?

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. Make a sketch, or actually cut out a 30° sector of a circle with scissors and shape the cone.
Did you notice that the arc length of the sector becomes the circular base of the cone and the radius of your sector becomes the slant height of the cone?
Find the perimeter of your original circle: 2π(6) = 12π cm
your sector angle of 30° is 30/360 of that
arc length of sector = 30/360 (12π) = π cm

So perimeter of cone base = π cm
2πr = π
r = 1/2 cm
let the height of the cone be h
h^2 + r^2 = 6^2
h^2 = 36 - 1/4 = 143/4
h = √143/2 = appr 5.98 cm

check my arithmetic

1. 👍
2. 👎
3. ℹ️
4. 🚩
👤
Reiny