A cube has a surface area of 486 m^2. What is the longest stick that can fit into the cube?  

Expert Answers

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The surface area of a cube of side s is given by 6*s^2 . Here the surface area is 486 m^2

6*s^2 = 486

=> s^2 = 486 / 6

=> s = sqrt 81

=> s = 9

The diagonal length of a cube of side 9 is sqrt (9^2 + 9^2 + 9^2) = sqrt 243 = 9*sqrt 3

The longest stick that can be placed in the cube is along a diagonal which is 9*sqrt 3 m  long.

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