Imagine a right circular cone with altitude H and slant height R. Let the radius of
the circular base be r. Imagine that the apex angle of the cone is . Now slit the
cone open by cutting along the slant height from the base to the apex. Unwrap the
slit cone to reveal a circular sector. Find the central angle of this sector, , as a
function of .
the radius of circular sector = slant height R
surface area of cone = area of a sector
surface area of cone:
area of a sector:
for apex angle of the cone:
then:
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