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Ganesh Prasadh from Jawahar Senior Secondary School, asked a question
Subject: Math , asked on 13/12/11

 Show that the semi-vertical angle of the cone fo masimum volume and of given slant height is tan inverse root 2

EXPERT ANSWER

Aakash Sharma , Meritnation Expert added an answer, on 14/12/11
2727 helpful votes in Math

Dear Student!

Here is the answer to your query.

 

 

Let α be the semi vertical angle of a cone of slant height l

Then V O = l cos α and OA = l sin α

 

Let V be the volume of the cone Then

 

for maximum or minimum V, we must have

 

Differentially (1) w. r. t. α we get

 

The V is maximum when tan α = or α = tan–1

 

i.e. when the semi vertical angle of the cone is tan–1

 

Cheers!

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Ganesh Prasadh From Jawahar Senior Secondary School, added an answer, on 14/12/11

Thank you Sir

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