Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere is -
Text Solution
Verified by ExpertsThe correct answer is:
A
Let h be the height of the cone and r be its radius.
∴ h = CL = CO + OL = a + OL
∴ OL = h – a
r = LA = √ (OA 2 – OL 2 )
or r = √ {a 2 – (h – a) 2 } = 
V = 
π r 2 h = 
π (2ah – h 2 ) h
= 
π (2ah 2 – h 3 )
dV/dh = ( π /3) (4ah – 3h 2 ) = 0
∴ h = 0 or 4a/3
h = 0 is rejected ⇒ h = 4a/3 = (2/3) (2a)
h = 
(diameter).
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