SOLUTION: A cone of height 12cm has a volume of n cm cubed and a curved surface area of n cm squared. Find the vertical angle of the cone.
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Question 1156779: A cone of height 12cm has a volume of n cm cubed and a curved surface area of n cm squared. Find the vertical angle of the cone.
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
where l is the slant height.
The volume and the lateral surface area are numerically equal:
The radius of the cone r and the slant height 4r form a right triangle with the altitude of the cone. The angle in that triangle at the vertex of the cone is half the vertical angle of the cone; the sine of that angle is r/(4r) = 1/4.
The vertical angle of the cone is
= approximately 28.955 degrees.
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