Final answer:
To calculate the volume of a dilated cube, we scale the original side length by the dilation factor and then cube it. The original volume is 75 cm3, and the dilation factor is 5, so the new volume is 9375 cm3.
Step-by-step explanation:
The question asks for the volume of a cube when it is dilated by a factor of 5. The original volume of the cube is 75 cm3. To find the volume of the dilated cube, we need to consider that dilation scales all dimensions of a geometric figure by a factor, which in this case is 5. Hence, we would need to increase each dimension of the original cube by a factor of 5 and then calculate the volume of the new cube.
First, we find the side length of the original cube by taking the cube root of the volume: V = s3, so s = ∛(V). The side length (s) of the original cube is thus the cube root of 75 cm3. After finding the original side length, we multiply it by the dilation factor of 5 to get the new side length. The volume of the dilated cube is then (5s)3.
The precise calculation involves cubing the dilation factor as well: (53) × original volume = 125 × 75 cm3. Therefore, the volume of the dilated cube is 9375 cm3. This demonstrates how three-dimensional scaling affects volume by the cube of the scale factor.