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MATHMAA

# Volume

Q)  Find the height of the cylinder with maximum possible Volume, if a cylinder is inscribed in a sphere with radius 6.

Sol)  Volume of cylinder (V) = $$\prod r^{2} h$$

Then we get  right triangle of hypotenuse of 6(radius of sphere) other two legs one is radius of cylinder x and other is half of height of cylinder h/2.

We get  $$x^{2}+\left ( \frac{h}{2}\right )^{2}=6^{2}$$