A 240° sector of a circle of radius 14cm is bent to form a cone.find the radius of the base of the cone, and it vertical angle.
2 answers
Answer the question please
Make a sketch to see that the arc length of the sector becomes the circumference of the circular base of the cone, and the radius of the sector
becomes the slant height of the cone.
arc length = (240/36)(2π)(14) = 56/3 π cm
so for radius R of the cone's base:
2πR = 56/3 π
R = 28/3 cm
Height of cone, call it h:
h^2 + (28/3)^2 = 14^2
h = ....
tan(half of vertical angle) = 14/(28/3) = 3/2
half of vertical angle = ....
vertical angle = .....
becomes the slant height of the cone.
arc length = (240/36)(2π)(14) = 56/3 π cm
so for radius R of the cone's base:
2πR = 56/3 π
R = 28/3 cm
Height of cone, call it h:
h^2 + (28/3)^2 = 14^2
h = ....
tan(half of vertical angle) = 14/(28/3) = 3/2
half of vertical angle = ....
vertical angle = .....
1 answer