a cube of sides 5 cm is painted on all its faces.if it is sliced in to a 1 cm3.cubes how many 1cm3 cubes will have exactly one of their faces painted?
6 * 5 * 5 immediately six sides with 5*5 each but the ones on the edges have two faces painted
so
6 * 4 * 4
Look at one of the faces, it will be 5 cm by 5 cm
The edges will be painted on two sides, while the 4 corners are actually painted on three sides.
So the only cubes painted on one side only are the inside squares of that face.
It will be 3 cm by 3 cm, for 9 of those
But there are 6 faces to a cube.
So cubes painted on only 1 side are 36.
of course 9 x 6 = 54, not 36
Yes, of course, 6*3*3
To determine the number of 1 cm^3 cubes that will have exactly one of their faces painted, we first need to calculate the number of cubes on the surface of the bigger cube.
A cube has 6 faces, and each face is a square. Given that each side of the larger cube is 5 cm, we can calculate the total number of cubes on the surface by finding the number of cubes on each face and then summing them.
The number of cubes on each face is obtained by dividing the length of the side of the larger cube (5 cm) by the length of a side of a smaller cube (1 cm):
Number of cubes on each face = (5 cm / 1 cm)^2 = 5^2 = 25 cubes on each face
Since there are 6 faces on a cube, the total number of cubes on the surface is:
Total number of cubes on surface = Number of cubes on each face × Number of faces
= 25 cubes on each face × 6 faces
= 150 cubes on the surface
However, when the larger cube is sliced into smaller 1 cm^3 cubes, only the edge cubes will have exactly one face painted. The interior cubes will have multiple faces painted.
The number of edge cubes on the surface of the larger cube can be calculated using the formula:
Number of edge cubes = 4 * edge length
Since each edge of the larger cube is 5 cm long, the number of edge cubes is:
Number of edge cubes = 4 * 5 = 20 cubes on the edges
Therefore, out of the 150 cubes on the surface, only 20 cubes will have exactly one face painted.