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,

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step-by-step explanation:

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8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.