Answer :
We know that total surface area of the cone = S = πr(l + r) …(1)
and Volume of the cone(V) =
Then by (1), we get,
P = V2
Now, differentiating P with respect to r, we get,
Now, if, , then
S = 4πr2
Now again differentiating with respect to r, we get
Therefore, P is maximum when S = 4πr2
And V is maximum when S = 4πr2
⇒ πr(l + r) = 4πr2
⇒ l = 3r
SinƟ =
Therefore, semi-vertical angle of right circular cone of given surface area and maximum volume is .
Hence Proved.
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation


RELATED QUESTIONS :
If the sum of the
Mathematics - Board PapersA metal box with
Mathematics - Board PapersShow that a
RD Sharma - Volume 1Find the local ma
Mathematics - Board PapersProve that the se
Mathematics - Board PapersProve that the ra
Mathematics - Board PapersProve that the le
Mathematics - Board Papers