Final answer:
The sides of the new cube are three times longer than the sides of the original cube, as the ratio of their side lengths is 3 cm / 1 cm, which equals 3.
Step-by-step explanation:
To answer how many times longer the sides of the new cube are compared to the sides of the original cube, we will use the information given about the side lengths and volumes of the cubes. According to the provided data, the smaller cube has a side length of 1 cm, while the larger cube has a side length of 3 cm. The ratio of their side lengths is therefore 3 cm / 1 cm, which equals 3. This indicates that the sides of the larger cube are three times longer than the sides of the smaller cube.
In the context of a different example, Marta's original square has a side length of 4 inches, and the larger square has dimensions that are twice the first square, meaning its side length is 8 inches. The ratio of the side lengths of Marta's squares is 8 inches / 4 inches, which is also 2. This is called a scale factor, and it indicates how many times larger or smaller one object is compared to another.