+194 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?
+9466 The side length of the cube = s
The number of square units in the surface area of the cube = 6s2
The number of cubic units in the volume of the cube = s3
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...
6s2 = (1/6)s3
36s2 = s3
36 = s3 / s2
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 = s3
The side length of the square = √(the number of square units in the area of the square)
The side length of the square = √( s3 )
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
