Answer:
Required largest volume is 0.407114 unit.
Step-by-step explanation:
Given surface area of a right circular cone of radious r and height h is,
and volume,
To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,
subject to,
We know for maximum volume . So let be the Lagranges multipliers be such that,
And,
Substitute (3) in (2) we get,
Substitute this value in (1) we get,
Then,
Hence largest volume,