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Prove that the semi-vertical angle of …

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Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface area is cot–1 √2.

Posted by Sankara Narayanan 3 years, 11 months ago

CBSE > Class 12 > Mathematics

1 answers

Gaurav Seth 3 years, 11 months ago

Solution:

Let V be the given volume of cone.

V=Volume of cone =

h = Height of cone =

C=Curved surface area of cone = , where r is radius and l is slant height of cone.

C= , as l²= r²+ h²

For Maxima and Minima, derivative of C that is curved surface area should be equal to zero.

K=C²= π²r²(r²+h²)

K =

Differentiating both sides with respect to r

K' = 4π²r³ +

Putting , K'=0

Let A be the semi vertical angle of the cone.

Cot A =

Cot A=

Hence proved.

0Thank You

ANSWER

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