The vertex of a cone is 60°. find the ratio of diameter with the height of the cone.
Answers
Answer: The vertex of a cone is 60°. the ratio of diameter with the height of the cone. is 2:√3.
Step-by-step explanation:
Given the vertex angle of a cone is 60° The angle formed by the cone's height and slant height is known as the semi-vertical angle and it is half of the vertical angle. We also know that the tan is defined as the ratio of perpendicular and base in the right-angled triangle.
So, the angle between the height and radius is half of the vertical angle. i.e., 30degree
tan a = BC/AC
Tan 30° = r / h
we know that tan 30° = 1/√3
substitute it and we get
1/√3 = r/h
h = r/√3
diameter of cone/ height of the cone = 2r / r/√3
diameter of cone/ height of the cone = 2/ √3.
hence , the ratio of diameter of cone to height of the cone is 2 : √3
To know more about cone from the given link
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