Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Show that the volume of the greatest cylinder which can be inscribed in a cone of height ' h ' and semi − vertical angle α is 
π h 3 tan 2 α .
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let H,R,V be
height, radius (base),
volume respectively of cylinder.
tan α = 
(0 < H < h)
V = π R 2 H
= π tan 2 α (h – H) 2 H
= π tan 2 α (h – H) (h – 3H)
V is maximum when H = 
.
Maximum V = π tan 2 α 
= 
h 3 tan 2 α .
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
If f(x) = cos π x + 10x + 3x 2 + x 3 , – 2 ≤ x ≤ 3 then absolute minimum value of f(x) is-
The function f(x) = x 5 – 5x 4 + 5x 3 – 1 has-
The function f(x) = has no extrema. if (n ∈ z)
If x exceeds by its square by the greatest possible quantity then x is-
An extreme value of the function
f(x) = (sin –1 x) 3 + (cos –1 x) 3 (–1 < x < 1) is
Let f(x) = (t + 4) 4 log (t+ 1) dt, then -