Reasoning Janice said that if you cut a cube into two parts you form 2 smaller cubes. Ling said that 2 rectangular prisms are formed. Who is correct? Explain.
What do you think?
Imagine cutting a cube in half. What will you get?
http://www.thinkgeek.com/images/products/zoom/rubix_cube.jpg
In case you still can't get the answer. It's 2 rectangular prisms.
Reasoning being:
Imagine a cube with all height, width and depth of 4. The volume would be equal to 4x4x4=64
now if you cut that cube in half, you get a volume of 32 or.. 4x4x2. That area is not cubic (cubic areas are always x^3). So it must be rectangular
In order to determine who is correct between Janice and Ling, we need to think about the properties of a cube and the result of cutting it into two parts.
A cube is a three-dimensional shape with six equal square faces. Each face of the cube is congruent to the others, and all angles within the cube are right angles. When we cut a cube into two parts, we need to think about how the resulting pieces would look.
Janice is correct in saying that when you cut a cube into two parts, you form two smaller cubes. Imagine cutting the cube along a plane that goes through its center, dividing it into two equal halves. Each half will still possess the properties of a cube, with all sides being congruent squares. Thus, we will end up with two smaller cubes.
On the other hand, Ling's claim that two rectangular prisms are formed is incorrect. A rectangular prism is a three-dimensional shape with six rectangular faces. If we were to cut a cube into two parts in a way that does not result in cubes, we would have to cut it unevenly or at a different angle. However, in the given scenario, we are considering cutting the cube into two equal halves, resulting in two cubes.
Therefore, Janice's statement is supported by the properties of a cube, making her correct in this case.