Suppose we have a godown to store grains. We know the weight and volume of the grains. We know the surface area of the storage space. Then we can calculate the height to which the stored bags will reach. We will know if the height we have is enough or not.
Suppose we have a cube shaped water tank on top of a building. Then we want to know the volume of water that can be filled in that. When we know the volume of water that we need each day. We want to construct a tank in a cubic shape. Then we can find the dimensions of the tank by cube root.
When we have to make sweets in the shape of a sphere or a cube. We have a given volume and weight of the sweet prepared. Then we know the number of sweets pieces made. This requires cubing. Also to calculate the size of a sweet piece either sphere or cube, we calculate its size in weight and then in volume. Then we find the dimension by cube root.
When we work with planets and Earth, the calculation of volume, density, radius need cube and cube roots.