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.
Cut it into 64 thin slices. They will be identical.
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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?
Every side will be equal on a cube. The volume of a cube is width x length x height4x4x4 = 43 = 64 cm3
Edge of the larger cube = 32 cm Volume of the larger cube = (32 cm)3 = 32768 cm3 Edge of the smaller cube = 4 cm Volume of the smaller cube = (4 cm)3 = 64 cm3 Since the smaller cubes are cut from the larger cube, volume of all of them will be equal to that of the larger cube. ∴ Total number of smaller cubes × Volume of the smaller cube = Volume of the larger cube ⇒ Total number of smaller cubes = Volume of the larger cube ÷ Volume of the smaller cube ⇒ Total number of smaller cubes = 32768 ÷ 64 = 512 Thus, 512 smaller cubes can be cut from the larger one.
cube root of 64 = 4 4 x 4 = 16, and 16 x 4 = 64 4 cube = 64
the cube root of 64 =4
64
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.
The volume of a cube is given by side^3, where side is the length of one side of the cube. So, if the volume of the cube is 64 cm^3, then side^3 = 64 cm^3. Solving for side, we get side = 4 cm. Since the cube has equal sides, the height (or length of any side) of the cube is 4 cm.
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
The fourth positive cube number is 4x4x4 which equals the number 64.