Q: How many 1 inch cubes are created when you cut a 4 inch cube into equal pieces of 1 inch cubes?

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54

There are 27 1x1cm cubes

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The cube root of the expression 403 is 40 itself. This follows from the definition of cubes and cube roots.

No. Each piece of the cube would have the same density.

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this cube is cut into 64 equal pieces....................................asdflkasufoiwerflkasdjf;laskudof

It can be.

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?

No because cubes do not have opposite sides that are different lengths. Cubes have all equal sides and all equal coners. A cube is not a rectangle.

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Cubes may be any size as long as they have six equal sides.

Breaking an ice cube into smaller pieces does not change its identity as ice; it is still made of the same substance, which is water in its solid state. The physical arrangement of the ice cube has changed, but its chemical composition remains the same.

Assuming that the cubes are 1x1x1, there will be one thousand cubes in the larger cube.

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.

Edges . . .Each cube . . . 12Four cubes. . . 48Vertices . . .Each cube . . . 8Four cubes . . 32

The equation for the number of 1 cm3 cubes to form a n3 cm3 hollow cube (n>1): 6n2-12n+8 (hint: cubes have 6 faces, 12 edges, and 8 vertices) I'm not sure whether you are asking about a 10 cm3 cube or a 103 cm3 cube. Since you can't divide a 10 cm3 cube into 1 cm3 pieces, I am going to assume you mean a 103 cm3 cube. This cube will yield 1000 1 cm3 cubes. For n=13, 6n2-12n+8 = 866 For n=14, 6n2-12n+8 = 1016 So, with 1000 little cubes, you can form a 13x13x13 cm hollow cube with 134 little cubes left out.