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Show that the vertical angle of a right circular cone of minimum curved surface that circumscribes a given sphere is 2sin -1 (^2-1).

Show that the vertical angle of a right circular cone of minimum curved surface that circumscribes a given sphere is 2sin-1(^2-1).

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
The formula of curved surface area of right circular cone is : pi*r*l
where r is the radius of and l is the slant height.
or
S = pi*x*(root(a^2 + x^2)
Solve for differentiation of S and equate it to zero since curved surface area is given as minimum.
that is dS/dx = 0

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