JEE Main 2019 — Application Of Derivatives Question with Solution
From: JEE Main 2019 (Online) 8th April Evening Slot
Question
The height of a right circular cylinder of maximum
volume inscribed in a sphere of radius 3 is
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Here r = 3 cos
and = 3 sin
h = 6 sin
We know, Volume of cylinder
V = r2 h
V = (9cos2)(6 sin)
V = 54 (sin - sin3)
For maxima/minima of volume,
cos - 3sin2 cos = 0
cos(1 - 3sin2) = 0
cos = 0
= (not possible)
or 1 - 3sin2 = 0
sin =
h = 6 sin = =
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