How deep should you place the wick of a spinning top with a angle of  80 degree to create a circular impression in the wood that has a diameter of 0.845 cm?



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Posted on (Answer #1)

From the center of the circular base draw a segment to the apex (wick) of the cone (spinning top.)

The distance from the center of the circle to the edge is .4225cm (since this is a radius, and radii are half the diameter.) Let the length of the segment drawn be h.

The angle formed by the segment and the side of the cone is `40^@` .

**Note that the triangle formed by the cross-section is an isosceles triangle and since h is perpendicular to the base h is also the angle bisector of the apex angle.**

Then we have a right triangle with legs h and .4225 and acute angle adjacent to h of 40 degrees.

So `tan40^@=.4225/h==>h=.4225/(tan40^@)`

Then `h~~.5035`


The depth of the wick should be .5035cm


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