SOLUTION: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a right-circular cone with a radius of 5 cm and a height of 12 cm.

Question 1191566: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a right-circular cone with a radius of 5 cm and a height of 12 cm.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a 2-dimensional sketch of a right circular cylinder inscribed in a right circular cone.

We are given AD = 5 and CD = 13, so we can conclude AC = 12.

Let x be the radius of the cylinder, BE. Similar triangles ACD and BCE give us BC = (12/5)x = 2.4x. The height of the cylinder is then 12-2.4x.

Express the volume of the cylinder in terms of x and maximize the volume by finding where the derivative of the volume function is 0.

The volume is maximum when the radius of the cylinder is 10/3.

That makes the height

ANSWER: radius 10/3; height 4

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