SOLUTION: A conical paper funnel of radius 4 and height 6 units is needed to make a good cup of coffee. If this funnel is made out of a sector of a circle, what must be the radius of this ci

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Question 1106590: A conical paper funnel of radius 4 and height 6 units is needed to make a good cup of coffee. If this funnel is made out of a sector of a circle, what must be the radius of this circle and what must be central angle of the sector?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


When the sector of a circle is formed into a cone, the radius of the sector becomes the slant height of the cone, and the length of the curved part of the sector becomes the circumference of the base of the cone.

The slant height of the cone, from the Pythagorean Theorem, is sqrt%284%5E2%2B6%5E2%29+=+sqrt%2852%29+=+2%2Asqrt%2813%29. So the radius of the sector is 2*sqrt(13).

The circumference of the base of the cone is 4%2A2%28pi%29; the circumference of the whole circle of which the sector is a part is %282%2Asqrt%2813%29%29%2A2%28pi%29.

The fraction of the whole circle that the sector is is then 4%2F%282%2Asqrt%2813%29%29+=+2%2F%28sqrt%2813%29%29; that means the measure of the central angle in radians is %282%2F%28sqrt%2813%29%29%29%2A2pi, or in degrees %282%2F%28sqrt%2813%29%29%29%2A360.