**Let cylinder of base radius r and height h**_{1} is included in a cone of height h and semi-vertical angle α.

**Then,**

AB = r,

OA = (h - h_{1}),

**In right angle triangle OAB,**

**Differentiating with respect to h**_{1},we get

**For maximum volume V, **

**\(\frac{dV}{dh_1}=0\)**

**Again differentiating with respect to h**_{1}, we get