Question
We are given a sectorwith radius 8cm and an angle of 156°. The sector is bent form a right cone
a) Calculate the radius of the cone
b) vertical angle of the cone
a) Calculate the radius of the cone
b) vertical angle of the cone
Answers
GPT 3.5
a) The circumference of the base of the cone is the same length as the curved edge of the sector.
Circumference of the base of the cone = 2πr
Curved edge of the sector = 2π(8) (since the radius of the sector is 8cm) = 16π cm
Setting them equal to each other:
2πr = 16π
r = 8 cm
Therefore, the radius of the cone is 8 cm.
b) The angle at the vertex of the cone is the same as the angle of the sector, which is 156°. The vertical angle is always twice the angle at the apex of the cone.
Vertical angle = 2(156°) = 312°
Therefore, the vertical angle of the cone is 312°.
Circumference of the base of the cone = 2πr
Curved edge of the sector = 2π(8) (since the radius of the sector is 8cm) = 16π cm
Setting them equal to each other:
2πr = 16π
r = 8 cm
Therefore, the radius of the cone is 8 cm.
b) The angle at the vertex of the cone is the same as the angle of the sector, which is 156°. The vertical angle is always twice the angle at the apex of the cone.
Vertical angle = 2(156°) = 312°
Therefore, the vertical angle of the cone is 312°.