Why is LPG stored in spherical tanks?

Because it's stored under pressure, all pressurised gas containers are cylindrical or spherical to eliminate corners which would be the weakest point.

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A sphere is a very strong structure. The even distribution of stresses on the sphere's surfaces, both internally and externally, generally means that there are no weak points. That's why a drop of water forms a spherical shape when under free fall, in short, it achieves a shape where all the resultant stresses neutralize when no external force(gravity) is acting on it. Moreover, they have a smaller surface area per unit volume than any other shape of vessel. This means, that the quantity of heat transferred from warmer surroundings to the liquid in the sphere, will be less than that for cylindrical or rectangular storage vessels. Thus less pressurization due to external heat.

Bhaumick...