A cube made up of 125 smallcubesthreeadjcent facecoloured with
red remaing 3 coloured with green
( Differentcolours, samecolour)
a) How manysmallcubes will have 3 faces painted?
b) How manysmallcubes will have 2 faces painted?
c) How manysmallcubes will have1 face painted?
d) How manysmallcubes will have 0 faces painted?
e) How manysmallcubes haveatleast two colours ?
F) How manysmallcubes haveatleast onecolour?
g) How manysmallcubes haveatmost two colours ?
h) How manysmallcubes haveatmost onecolour?
right ans with right explanation will be marked as brainliest
Answers
Answer:
Each side will be 1251/3=51251/3=5 small cube lengths long (I will use “cube length” in place of “small cube length” hereafter). One way of doing it is to imagine the larger cube has a “shell” of cube length 11 around it. Each side used to be 55 cube lengths long, but if we take away the “shell”, we have to subtract one cube length twice for each side (once for each end of the side). Thus the resulting cube with no “shell” has three sides of cube length 33. This cube with no shell has a volume of 33=2733=27. There are 2727 little cubes with no colored faces.
Another way of doing it: 5×5=255×5=25 cubes will be at the surface of one face of the cube (call it face A). 5×4=205×4=20 cubes will be at the surface of one of the four faces bordering face A of the cube (the cubes on the surface of face A AND one of the neighboring faces are not counted twice, that’s why it’s 5×45×4 and not 5×55×5). If we call it face B, we can say there are 2020 cubes on the surface of face B but not also on the surface of face A. So we count 2020 for one face neighboring face A, then 1616 for the next neighboring face (to avoid double counting the cubes on one edge), then 1616 again, then 1212 (we need to avoid double counting cubes on two edges). This gives 20+16+16+12=6420+16+16+12=64 cubes for the faces neighboring face A. Finally, 3×3=93×3=9 cubes are only on the surface of the remaining face and no other faces. Thus we have 125−25−64−9=27125−25−64−9=27 little cubes with no colored faces.
hope it helps you