Height of the cylinder of maximum volume that can be inscribed in a sphere of radius 12cm is
Answer (1)
16th Jan, 2021
Hello,
As per the question, we have to inscribe a cylinder into a sphere. Radis of sphere is = 12 cm
Let r is the radius and h is the height of this cylinder.
So when we make figure of this question, we found an equation i.e. (h/2)^2 + r^2 = R^2
Solving it we get , h = 2 ( √ R^2 - r^2 )
Now volune of cylinder V is = pi . r^2 . h
Put value of this h into this equation, we get
V = 2. pi. r^2. ( √ R^2 - r^2 )
We have to maximize this volume, so do dV/dr = 0
Solving it we get r^2 = 2. R^2/3
put R = 12 here, so r = 4√6
and h = 8√3
Hope it helps.
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