Question

Two opposite surfaces of a cube are painted red

and all other remaining surface are painted

green, now it is cut in such a way that 125 small

and equal cubes are formed. Based on this

information answer the questions given below.

97. How many cubes will have only one surface

painted and it is red?

a. 12

b. 18

c. 24

d. 27

98. How many cubes will have their two surface

painted one red and other green?

a. 24

b. 27
​

Answer 1

Step-by-step explanation:

Each side will be [math]125^{1/3} = 5[/math] 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 [math]1[/math] around it. Each side used to be [math]5[/math] 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 [math]3[/math]. This cube with no shell has a volume of [math]3^3 = 27[/math]. There are [math]27[/math] little cubes with no colored faces.