Which cube is a unit cube?
A. a cube that is 3 meters long, 3 meters wide, and 3 meters high
b. a cube that is 9 inches long, 9 inches wide, and 9 inches high
c. a cube that is 1 yard long, 1 yard wide, and 1 yard high
d. a cube that is 11 centimeters long, 11 centimeters tall, and 11 centimeters high
The correct answer and explanation is:
The correct answer is C. a cube that is 1 yard long, 1 yard wide, and 1 yard high.
A unit cube is defined as a cube whose sides are each of unit length. The unit length typically used is 1, but the unit can be any consistent measure of length, such as 1 inch, 1 meter, or 1 yard. In this case, the cube with each side measuring 1 yard is a unit cube, as it has equal sides of 1 unit of length (1 yard).
Let’s break down why the other options don’t fit the definition of a unit cube:
- Option A (3 meters long, 3 meters wide, and 3 meters high): While this is a cube, its side length is much larger than 1 unit, making it not a unit cube. In fact, it is a cube with side lengths of 3 meters, which are significantly larger than a unit length.
- Option B (9 inches long, 9 inches wide, and 9 inches high): Again, this is a cube, but its side length of 9 inches is much larger than 1 inch, so it is also not a unit cube. A unit cube would need sides of exactly 1 inch (or any other standard unit of measurement).
- Option D (11 centimeters long, 11 centimeters tall, and 11 centimeters high): While this is another cube, its side length of 11 centimeters is not 1 unit, and therefore it is not a unit cube either.
In summary, a unit cube is a cube with each side measuring exactly one unit of length, which is precisely what option C describes with its side lengths of 1 yard.