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# prism geometry

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Sally has a cube of side length $s$ units such that the number of square units in the surface area of the cube equals $\frac{1}{6}$ of the number of cubic units in the volume. She also wants to make a square for which the number of square units in the area of the square is equal to the number of cubic units in the volume of the cube. What should the side length of the square be?

Jan 9, 2021

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surface area of cube =  6side^2 = 6S^2   units

volume = S^3     units

So....

(6 S^2) units  =   S^3/6   units

36S^2   =  S^3          divide out S^2

36 =   S^2

S  =  6

Cubic units in volume  = 6^3   = 216

Side of  square she  wants to  construct =  sqrt (216)  =sqrt (36*6)  = 6 sqrt (6)  units

Jan 9, 2021