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How many smaller cubes are not painted at all if a cube is painted green on all sides & cut into 64 cubes of equal size?
Cube root of 64 is 4 therefore cube is 4 x 4 x 4. Each side of the cube has 16 visible small cube faces, 4 of which are corners (3 green sides) and 8 more are edges (2 green sides), so there are only four small cubes with one green face on each of the six sides of the large cube. Your answer is therefore 24.
Denoting a to be the cube's side, its volume is equal to a3. Therefore, if V = 64 in3:a = 641/3 = 4 inA cube has six faces, with each of their surface area being equal to a2; hence:Total area = 6 a2 = 96 in2
Cube root it. the square of a cubed number can be divided into 3 equal squares (Ae3)e2 = Ae(3x2) or Ae6 this is also equal to (Ae2)e3 as long as a number can be expresses as a root number with an exponent equal to 6 the cube root of that number is a square of the root Example: 64 can be divided into 8 x 8 or 4 x 4 x 4 64 is the square of 8 and the cube of 4 4 is the square of 2, 8 is the cube of 2 per the above formula: (2e3)e2 = 2e6 = (2e2)e3 = 8e2 and 4e3 more simply: 2 x 2 x 2 x 2 x 2 x 2 = 64 8 x 8 = 64 (64 is a square) 4 x 4 x 4 = 64 (64 is also a cube) 2 x 2 = 4 (4 is a square)
You need units, but the answer is 384 square Whatevers. The surface area of one side is 8*8 = 64 square Whatevers. A cube has 6 equal sides. 64*6 = 384.