The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What is the largest volume of a right circular cone if its surface area is S? Use Lagrange multipliers to solve the problem.

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,

it is true

step-by-step explanation:

all the combinations add up i used   calculator