Final answer:
The volume of the second cube, whose sides are half the length of the first cube which has a volume of 1,000 cubic units, is 125 cubic units since the volume of a cube with sides half the length of another is an eighth of the larger cube's volume.
Step-by-step explanation:
The question asks us to find the volume of a second cube when the sides of this cube are half the length of the first cube with a volume of 1,000 cubic units. The relationship between the sides of a cube and its volume is given by the formula V = s³, where V is the volume and s is the length of one side.
To determine the volume of the first cube, we find the cube root of 1,000, which gives us the length of one side of the first cube. If the first cube's side is s, then the second cube's side is s/2 because it's half as long. Hence, the volume of the second cube would be ((s/2)³), which is one eighth of the volume of the first cube because (1/2)³ is 1/8. So, the second cube's volume is 1,000/8 = 125 cubic units.