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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?

Mar 17, 2018

#1
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Let the side of the cube =S

SA of a cube =6 x S^2

V of a cube =S^3

S^3/6 = 6S^2

S^3 =36S^2 divide both sides by S^2

S = 36 - the side of the cube

V of cube =36^3 =46,656 cubic units.

Area of a square =S^2 - square units.

Sqrt(46,656) = 216 - units - side length of the square.

Mar 17, 2018
edited by Guest  Mar 17, 2018

#1
+2

Let the side of the cube =S

SA of a cube =6 x S^2

V of a cube =S^3

S^3/6 = 6S^2

S^3 =36S^2 divide both sides by S^2

S = 36 - the side of the cube

V of cube =36^3 =46,656 cubic units.

Area of a square =S^2 - square units.

Sqrt(46,656) = 216 - units - side length of the square.

Guest Mar 17, 2018
edited by Guest  Mar 17, 2018