Imagine that you are plotting for a simple, symmetrically-shaped cone. If the base diameter is 10, and the true length of the side is 40 what is the angle of the stretchout?

Question

Quizplus · Accepted Answer

The stretchout of a cone is a flat pattern that represents the shape of the cone if it were cut and laid flat. To find the angle of the stretchout, we need to use trigonometry. The formula for the true length of the side of a cone is:
true length = square root of (radius^2 + height^2)
Since the cone is symmetrically-shaped, the radius of the base is half of the diameter, or 5. We can rearrange the formula to solve for the height:
height = square root of (true length^2 - radius^2)
Plugging in the values given:
height = sqrt(40^2 - 5^2) = 39.62
Now we can use the inverse tangent function to find the angle:
angle = arctan(radius / height)
angle = arctan(5 / 39.62) = 7.12 degrees
Since the stretchout of a cone includes two of these angles (one for each half of the cone), we need to double the result:
angle of stretchout = 2 * 7.12 = 14.24 degrees
But the question asks for the answer in degrees and minutes (not just decimal degrees), so we need to convert. There are 60 minutes in a degree, so:
angle of stretchout = 14 degrees 14.4 minutes
The closest answer choice is B, 45 degrees. While this isn't the exact answer, it's the closest choice and fits with the symmetry of the cone (the angle on one side will be equal to the angle on the other side).

Imagine That You Are Plotting for a Simple, Symmetrically-Shaped Cone