When Flat Math Gets Deep

Volumes of shipping boxes, liquid in bottles, concrete in foundations — all three-dimensional. The formulas (V = lwh for boxes, V = pi times r squared times h for cylinders, V = 4/3 times pi times r cubed for spheres) are the working vocabulary of engineering.

A doctor calculating a drug dosage considers the patient's body volume. A shipping company optimizes 3D packing so trucks leave with the least empty air. An architect chooses between a square room and a round one partly based on the surface-to-volume ratio that affects heating costs.