SOLUTION: A rectangular prism has a surface area of 256 sq in. What is the maximum volume it can hold?
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Question 399060: A rectangular prism has a surface area of 256 sq in. What is the maximum volume it can hold?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose the dimensions of the prism are L, W, H. Then,
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By the AM-GM inequality (arithmetic mean - geometric mean inequality),
Cubing both sides,
, this value is the maximum volume of the prism, which occurs when the solid is a cube.
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