Sally has a cube of side length s units such that the number of square units in the surface area of the cube equals 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?

Confusedperson
Jun 21, 2018

#1**+1 **

The side length of the cube = s

The number of square units in the surface area of the cube = 6s^{2}

The number of cubic units in the volume of the cube = s^{3}

The number of square units in the surface area of the cube equals 1/6 of the number of cubic units in the volume. So...

6s^{2} = (1/6)s^{3}

36s^{2} = s^{3}

36 = s^{3} / s^{2}

36 = s

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. So...

The number of square units in the area of the square = s^{3}

The side length of the square = √(the number of square units in the area of the square)

The side length of the square = √( s^{3} )

The side length of the square = s √s

The side length of the square = 36 √36

The side length of the square = 36 * 6

The side length of the square = 216

hectictar
Jun 21, 2018