A right circular cone has a given curved surface A. Show that when its volume is maximum the ratio of the the height to the base radius is √2:1 ?
1 Answer
Explanation:
.
The formula for the curved surface area of a cone which does not include the area of the base is:
From the right angle triangle shown, using Pythagoras' formule, we get:
Therefore, the curved area
The volume formula is:
Let's solve for
To find the maximum volume, we take the derivative of the volume function and set it equal to
Let's substitute for
Dividing both sides by