What is the formula for calculating the central angle of a cone?

In summary, the central angle of a cone is the angle formed by two radii at the center of the cone. It can be calculated by dividing the arc length of the base by the base radius. The central angle is directly proportional to the surface area of the cone. It cannot be greater than 360 degrees as it would result in overlapping surfaces. The central angle does not directly affect the volume of the cone, but a larger angle may result in a different volume depending on the dimensions of the cone.
  • #1
ivan77
17
0
Hi,

If you have a cone (right angle) with radius r, slant length l, how is the central angle theta = 2*pi*r/l?

Thanks,

Ivan77
 
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  • #2
Realized the problem. It boils down to the formula for a arclength s = theta*radius (circle) where s is 2*pi*r (r is the radius of the cone) and the l is the radius of the circle.
 

What is the central angle of a cone?

The central angle of a cone is the angle formed by the intersection of two radii at the center of the cone.

How do you calculate the central angle of a cone?

The central angle of a cone can be calculated by dividing the arc length of the base of the cone by the radius of the base.

What is the relationship between the central angle and the surface area of a cone?

The central angle of a cone is directly proportional to the surface area of the cone. As the central angle increases, the surface area also increases.

Can the central angle of a cone be greater than 360 degrees?

No, the central angle of a cone cannot be greater than 360 degrees because it would result in overlapping and self-intersecting surfaces.

How does the central angle of a cone affect the volume of the cone?

The central angle of a cone does not have a direct effect on the volume of the cone. However, a larger central angle may result in a wider and shorter cone, which would have a different volume than a narrower and taller cone with the same base radius.

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