Q. 27 5.0( 2 Votes )

Show what the maximum volume of the cylinder which can be inscribed in a sphere of radius cm is 500 π cm3 .

Answer :

The maximum volume cylinder will be carved when the diameter of sphere and the axis of cylinder coincide.

Let h be the height of our cylinder.

r be the radius of the cylinder.

R = 53 radius of the sphere

OL = x

H = 2x


Volume of cylinder V = πr2h


x = - 5 cannot be taken as the length cannot be negative.

At x = 5, we have to check whether maxima exits or not.


At x = 5, is negative. Hence, maxima exits at x = 5.

Therefore, at x = 5

Volume of Cylinder = π(75 - x2)(2x)

Volume = π(75 - 25)(10) = 500π

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.