Final answer:
The height of shape B is not 10 times the height of shape A, but rather the cube root of 10 times that height, due to the volume being a function of the cube of linear dimensions for similar geometric shapes.
Step-by-step explanation:
When comparing two similar solid shapes with a volume ratio of 1:10, it's important to understand that if the shapes are similar, their dimensions must be proportional. If shape A and shape B have a volume ratio of 1:10, we can denote the scaling factor for linear dimensions as k. Since volume is a function of the cube of the linear dimensions in geometrically similar shapes, this means that k^3 = 1:10. Therefore, k would be the cube root of 10, not 10 itself, leading to the conclusion that the height of shape B is not 10 times the height of shape A, but rather the cube root of 10 times the height of shape A.
For an explicit example considering a cube and a sphere, if each shape has the same volume, the ratio of surface area to volume will be different for both shapes. As per the given references, the surface area to volume ratio is influenced by the shape of the object and this ratio will be different for a sphere, a cube, and a cylinder even if they have the same volume.